diff --git a/paddle/fluid/framework/distributed_strategy.proto b/paddle/fluid/framework/distributed_strategy.proto
index fff78dd872c99f2b9ec9a5998ce43f2f6ad8e40b..94753f8dd38e09a4038986fac2f6103896fe59c8 100644
--- a/paddle/fluid/framework/distributed_strategy.proto
+++ b/paddle/fluid/framework/distributed_strategy.proto
@@ -120,6 +120,7 @@ message BuildStrategy {
   optional bool fix_op_run_order = 13 [ default = false ];
   optional bool allow_cuda_graph_capture = 14 [ default = false ];
   optional int32 reduce_strategy = 15 [ default = 0 ];
+  optional bool fuse_gemm_epilogue = 16 [ default = false ];
 }
 
 message ExecutionStrategy {
diff --git a/paddle/fluid/framework/ir/fuse_gemm_epilogue_pass.cc b/paddle/fluid/framework/ir/fuse_gemm_epilogue_pass.cc
index f48224cbdc24fe9706a3c4eae029c6dc35381ad2..b72a63d37853c04ead4547ae4c384c5282c8abcd 100644
--- a/paddle/fluid/framework/ir/fuse_gemm_epilogue_pass.cc
+++ b/paddle/fluid/framework/ir/fuse_gemm_epilogue_pass.cc
@@ -22,6 +22,12 @@ namespace paddle {
 namespace framework {
 namespace ir {
 
+static void GetTransposeAttrsFromOp(const OpDesc &op, bool *trans_x,
+                                    bool *trans_y) {
+  *trans_x = BOOST_GET_CONST(bool, op.GetAttr("trans_x"));
+  *trans_y = BOOST_GET_CONST(bool, op.GetAttr("trans_y"));
+}
+
 void FuseGemmEpiloguePass::ApplyImpl(ir::Graph *graph) const {
   EpiloguePassActivationCache cache;
 
@@ -75,6 +81,9 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearFwd(ir::Graph *graph,
     if (!IsGemmFromLinear_(matmul_x_shape, matmul_w_shape, matmul_op_desc))
       return;
 
+    bool trans_x, trans_y;
+    GetTransposeAttrsFromOp(*matmul_op_desc, &trans_x, &trans_y);
+
     OpDesc fused_gemm_epilogue_op_desc(matmul_op->Op()->Block());
     std::string activation = "none";
     fused_gemm_epilogue_op_desc.SetType("fused_gemm_epilogue");
@@ -85,6 +94,8 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearFwd(ir::Graph *graph,
     fused_gemm_epilogue_op_desc.SetAttr("activation", activation);
     fused_gemm_epilogue_op_desc.SetAttr("op_role",
                                         matmul_op_desc->GetAttr("op_role"));
+    fused_gemm_epilogue_op_desc.SetAttr("trans_x", trans_x);
+    fused_gemm_epilogue_op_desc.SetAttr("trans_y", trans_y);
     auto gemm_epilogue_node = g->CreateOpNode(&fused_gemm_epilogue_op_desc);
 
     IR_NODE_LINK_TO(subgraph.at(x), gemm_epilogue_node);
@@ -154,6 +165,9 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearActFwd(
 
     auto activation = act_op->Op()->Type();
 
+    bool trans_x, trans_y;
+    GetTransposeAttrsFromOp(*matmul_op_desc, &trans_x, &trans_y);
+
     OpDesc fused_gemm_epilogue_op_desc(matmul_op->Op()->Block());
     fused_gemm_epilogue_op_desc.SetType("fused_gemm_epilogue");
     fused_gemm_epilogue_op_desc.SetInput("X", {subgraph.at(x)->Name()});
@@ -163,6 +177,8 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearActFwd(
     fused_gemm_epilogue_op_desc.SetAttr("activation", activation);
     fused_gemm_epilogue_op_desc.SetAttr("op_role",
                                         matmul_op_desc->GetAttr("op_role"));
+    fused_gemm_epilogue_op_desc.SetAttr("trans_x", trans_x);
+    fused_gemm_epilogue_op_desc.SetAttr("trans_y", trans_y);
 
     auto gemm_epilogue_node = g->CreateOpNode(&fused_gemm_epilogue_op_desc);
 
@@ -274,6 +290,9 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearBwd(ir::Graph *graph,
                            matmul_grad_op_desc))
       return;
 
+    bool trans_x, trans_y;
+    GetTransposeAttrsFromOp(*matmul_grad_op_desc, &trans_x, &trans_y);
+
     OpDesc fused_gemm_epilogue_grad_op_desc(ele_add_grad_op->Op()->Block());
     std::string activation_grad = "none";
     fused_gemm_epilogue_grad_op_desc.SetType("fused_gemm_epilogue_grad");
@@ -292,6 +311,8 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearBwd(ir::Graph *graph,
                                              activation_grad);
     fused_gemm_epilogue_grad_op_desc.SetAttr(
         "op_role", matmul_grad_op_desc->GetAttr("op_role"));
+    fused_gemm_epilogue_grad_op_desc.SetAttr("trans_x", trans_x);
+    fused_gemm_epilogue_grad_op_desc.SetAttr("trans_y", trans_y);
 
     auto gemm_epilogue_grad_node =
         g->CreateOpNode(&fused_gemm_epilogue_grad_op_desc);
@@ -394,6 +415,8 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearActBwd(
 
     auto activation_grad = act_grad_op->Op()->Type();
 
+    bool trans_x, trans_y;
+    GetTransposeAttrsFromOp(*matmul_grad_op_desc, &trans_x, &trans_y);
     OpDesc fused_gemm_epilogue_grad_op_desc(ele_add_grad_op->Op()->Block());
     fused_gemm_epilogue_grad_op_desc.SetType("fused_gemm_epilogue_grad");
     fused_gemm_epilogue_grad_op_desc.SetInput("DOut",
@@ -410,6 +433,8 @@ ir::Graph *FuseGemmEpiloguePass::FuseLinearActBwd(
                                              activation_grad);
     fused_gemm_epilogue_grad_op_desc.SetAttr(
         "op_role", matmul_grad_op_desc->GetAttr("op_role"));
+    fused_gemm_epilogue_grad_op_desc.SetAttr("trans_x", trans_x);
+    fused_gemm_epilogue_grad_op_desc.SetAttr("trans_y", trans_y);
 
     auto gemm_epilogue_grad_node =
         g->CreateOpNode(&fused_gemm_epilogue_grad_op_desc);
@@ -456,10 +481,6 @@ bool FuseGemmEpiloguePass::IsGemmFromLinear_(
       if (tmp_vec.size() > 0) return false;
     }
   }
-  if (BOOST_GET_CONST(bool, matmul_v2_op->GetAttr("trans_x")) ||
-      BOOST_GET_CONST(bool, matmul_v2_op->GetAttr("trans_y")))
-    return false;
-
   return true;
 }
 
diff --git a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cc b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cc
index 4c4e3661e6d6edc5ea95b77cd283cc99afcca8ed..7cb6777e5a79ac55d15bf369cd00957904541b01 100644
--- a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cc
+++ b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cc
@@ -13,6 +13,7 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License. */
 
+#include "paddle/fluid/operators/fused/fused_gemm_epilogue_op.h"
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/framework/op_version_registry.h"
 
@@ -208,6 +209,9 @@ class FusedGemmEpilogueGradOp : public framework::OperatorWithKernel {
     auto x_dims = ctx->GetInputDim("X");
     auto y_dims = ctx->GetInputDim("Y");
 
+    auto trans_x = ctx->Attrs().Get<bool>("trans_x");
+    auto trans_y = ctx->Attrs().Get<bool>("trans_y");
+
     PADDLE_ENFORCE_GE(
         dout_dims.size(), 2,
         platform::errors::InvalidArgument(
@@ -242,14 +246,14 @@ class FusedGemmEpilogueGradOp : public framework::OperatorWithKernel {
     auto x_mat_dims = phi::flatten_to_2d(x_dims, x_dims.size() - 1);
 
     PADDLE_ENFORCE_EQ(
-        dout_mat_dims[1], y_dims[1],
+        dout_mat_dims[1], trans_y ? y_dims[0] : y_dims[1],
         platform::errors::InvalidArgument(
             "The last dimension of DOut should be equal with Y's last"
             "dimension. But received DOut[-1] = [%d], Y[1] = [%d].",
             dout_mat_dims[1], y_dims[1]));
 
     PADDLE_ENFORCE_EQ(
-        dout_mat_dims[0], x_mat_dims[0],
+        dout_mat_dims[0], trans_x ? x_mat_dims[1] : x_mat_dims[0],
         platform::errors::InvalidArgument(
             "The first dimension of DOut should be equal with X's first"
             "dimension. But received DOut[0] = [%d], Y[0] = [%d].",
@@ -288,7 +292,7 @@ class FusedGemmEpilogueGradOp : public framework::OperatorWithKernel {
 
     if (ctx->HasOutput("DBias")) {
       std::vector<int64_t> dbias_dims;
-      dbias_dims.push_back(y_dims[1]);
+      dbias_dims.push_back(trans_y ? y_dims[0] : y_dims[1]);
       ctx->SetOutputDim("DBias", phi::make_ddim(dbias_dims));
     }
   }
@@ -323,6 +327,20 @@ class FusedGemmEpilogueGradOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("DBias",
               "The output grad tensor to bias of Out = (Act(X) * Y) + bias.")
         .AsDispensable();
+    AddAttr<bool>(
+        "trans_x",
+        R"DOC((bool, default false), Whether to transpose input tensor X 
+    or not. The input tensor X coulbe be more than two dimension. When 
+    set trans_x=true, it would fully reverse X. For instant: X with shpae 
+    [d0, d1, d2, d3] -> [d3, d2, d1, d0].)DOC")
+        .SetDefault(false);
+    AddAttr<bool>(
+        "trans_y",
+        R"DOC((bool, default false), Whether to transpose input tensor Y 
+    or not. The input tensor Y should be two dimension. When 
+    set trans_y=true, it would transpose Y. For instant: Y with shpae 
+    [d0, d1] -> [d1, d0].)DOC")
+        .SetDefault(false);
 
     AddAttr<std::string>(
         "activation_grad",
@@ -343,11 +361,38 @@ X with shape [d0, d1, d2, d3] -> X_2D with shape [d0*d1*d2, d3]
   }
 };
 
+template <typename T>
+class FusedGemmEpilogueOpGradMaker : public framework::SingleGradOpMaker<T> {
+ public:
+  using framework::SingleGradOpMaker<T>::SingleGradOpMaker;
+
+ protected:
+  void Apply(GradOpPtr<T> op) const override {
+    const auto& act_type = this->template Attr<std::string>("activation");
+    PADDLE_ENFORCE_EQ(act_type, "none", phi::errors::InvalidArgument(
+                                            "The activation should be none."));
+
+    op->SetType(this->ForwardOpType() + "_grad");
+    op->SetInput("X", this->Input("X"));
+    op->SetInput("Y", this->Input("Y"));
+    op->SetInput("DOut", this->OutputGrad("Out"));
+
+    op->SetOutput("DX", this->InputGrad("X"));
+    op->SetOutput("DY", this->InputGrad("Y"));
+    op->SetOutput("DBias", this->InputGrad("Bias"));
+
+    op->SetAttrMap(this->Attrs());
+  }
+};
+
 }  // namespace operators
 }  // namespace paddle
 
 namespace ops = paddle::operators;
-REGISTER_OPERATOR(fused_gemm_epilogue, ops::FusedGemmEpilogueOp,
-                  ops::FusedGemmEpilogueOpMaker)
+REGISTER_OPERATOR(
+    fused_gemm_epilogue, ops::FusedGemmEpilogueOp,
+    ops::FusedGemmEpilogueOpMaker,
+    ops::FusedGemmEpilogueOpGradMaker<paddle::framework::OpDesc>,
+    ops::FusedGemmEpilogueOpGradMaker<paddle::imperative::OpBase>);
 REGISTER_OPERATOR(fused_gemm_epilogue_grad, ops::FusedGemmEpilogueGradOp,
-                  ops::FusedGemmEpilogueGradOpMaker)
+                  ops::FusedGemmEpilogueGradOpMaker);
diff --git a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cu b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cu
index 9bf3d1a485efc71a19960525cb427ffb823eeefa..407cd2b974def8e8566672ea80bac9fd5d7491ba 100644
--- a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cu
+++ b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.cu
@@ -15,6 +15,7 @@ limitations under the License. */
 
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/framework/op_version_registry.h"
+#include "paddle/fluid/framework/scope_guard.h"
 #include "paddle/fluid/operators/fused/fused_gemm_epilogue_op.h"
 #include "paddle/fluid/platform/dynload/cublasLt.h"
 #include "paddle/fluid/platform/float16.h"
@@ -41,6 +42,8 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
     bool trans_y = ctx.Attr<bool>("trans_y");
 
     std::string activation = ctx.Attr<std::string>("activation");
+    VLOG(10) << "trans_x = " << trans_x << " , trans_y = " << trans_y
+             << " , activation = " << activation;
     bool enable_auxiliary = reserve_space == nullptr ? false : true;
 
     out->mutable_data<T>(ctx.GetPlace());
@@ -48,6 +51,7 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
 
     auto x_mat_dims =
         phi::flatten_to_2d(x->dims(), trans_x ? 1 : x->dims().size() - 1);
+    // (M * K) * (K * N)
     int64_t M = trans_x ? x_mat_dims[1] : x_mat_dims[0];
     int64_t K = trans_y ? y->dims()[1] : y->dims()[0];
     int64_t N = trans_y ? y->dims()[0] : y->dims()[1];
@@ -106,10 +110,11 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
           platform::dynload::cublasLtMatmulDescSetAttribute(
               operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_POINTER,
               &aux_data, sizeof(aux_data)));
+      int64_t aux_ld = N;
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
-              operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_LD, &N,
-              sizeof(N)));
+              operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_LD, &aux_ld,
+              sizeof(aux_ld)));
     }
 
     cublasLtMatrixLayout_t x_desc = NULL, y_desc = NULL, out_desc = NULL;
@@ -129,8 +134,7 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
         &out_desc, mat_type, N, M, N));
 
     cublasLtHandle_t lt_handle = dev_ctx.cublaslt_handle();
-    size_t workspace_size = 4 * 1024 * 1024;
-
+    size_t workspace_size = static_cast<size_t>(4) * 1024 * 1024 * 1024;
     cudaStream_t stream = dev_ctx.stream();
     memory::allocation::AllocationPtr workspace =
         memory::Alloc(dev_ctx, workspace_size);
@@ -149,13 +153,13 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
     const auto* y_data = y->data<T>();
     const auto* x_data = x->data<T>();
 
-    cublasLtMatmulAlgo_t algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
+    auto algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
         lt_handle, operation_desc, y_desc, x_desc, out_desc, alpha, beta,
         y_data, x_data, out_data, stream, workspace->ptr(), workspace_size);
 
     PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatmul(
         lt_handle, operation_desc, alpha, y_data, y_desc, x_data, x_desc, beta,
-        out_data, out_desc, out_data, out_desc, &algo, workspace->ptr(),
+        out_data, out_desc, out_data, out_desc, algo, workspace->ptr(),
         workspace_size, stream));
 
     PADDLE_ENFORCE_GPU_SUCCESS(
@@ -191,12 +195,94 @@ class FusedGemmEpilogueKernel : public framework::OpKernel<T> {
   }
 };
 
+enum FusedGEMMGradInType { kDX = 0, kDY = 1, kDZ = 2 };
+
+template <bool TransX, bool TransY>
+struct FusedGEMMGradTrait;
+
+template <>
+struct FusedGEMMGradTrait<false, false> {
+  static constexpr auto kXGradA = FusedGEMMGradInType::kDZ;
+  static constexpr auto kXGradB = FusedGEMMGradInType::kDY;
+  static constexpr auto kXGradATrans = false;
+  static constexpr auto kXGradBTrans = true;
+
+  static constexpr auto kYGradA = FusedGEMMGradInType::kDX;
+  static constexpr auto kYGradB = FusedGEMMGradInType::kDZ;
+  static constexpr auto kYGradATrans = true;
+  static constexpr auto kYGradBTrans = false;
+};
+
+template <>
+struct FusedGEMMGradTrait<true, false> {
+  static constexpr auto kXGradA = FusedGEMMGradInType::kDY;
+  static constexpr auto kXGradB = FusedGEMMGradInType::kDZ;
+  static constexpr auto kXGradATrans = false;
+  static constexpr auto kXGradBTrans = true;
+
+  static constexpr auto kYGradA = FusedGEMMGradInType::kDX;
+  static constexpr auto kYGradB = FusedGEMMGradInType::kDZ;
+  static constexpr auto kYGradATrans = false;
+  static constexpr auto kYGradBTrans = false;
+};
+
+template <>
+struct FusedGEMMGradTrait<false, true> {
+  static constexpr auto kXGradA = FusedGEMMGradInType::kDZ;
+  static constexpr auto kXGradB = FusedGEMMGradInType::kDY;
+  static constexpr auto kXGradATrans = false;
+  static constexpr auto kXGradBTrans = false;
+
+  static constexpr auto kYGradA = FusedGEMMGradInType::kDZ;
+  static constexpr auto kYGradB = FusedGEMMGradInType::kDX;
+  static constexpr auto kYGradATrans = true;
+  static constexpr auto kYGradBTrans = false;
+};
+
+template <>
+struct FusedGEMMGradTrait<true, true> {
+  static constexpr auto kXGradA = FusedGEMMGradInType::kDY;
+  static constexpr auto kXGradB = FusedGEMMGradInType::kDZ;
+  static constexpr auto kXGradATrans = true;
+  static constexpr auto kXGradBTrans = true;
+
+  static constexpr auto kYGradA = FusedGEMMGradInType::kDZ;
+  static constexpr auto kYGradB = FusedGEMMGradInType::kDX;
+  static constexpr auto kYGradATrans = true;
+  static constexpr auto kYGradBTrans = true;
+};
+
+static constexpr auto BoolToCuBlasEnum(bool transpose) {
+  return transpose ? CUBLAS_OP_T : CUBLAS_OP_N;
+}
+
 template <typename DeviceContext, typename T>
 class FusedGemmEpilogueGradKernel : public framework::OpKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
-    auto& dev_ctx = ctx.template device_context<platform::CUDADeviceContext>();
+    bool transpose_x = ctx.Attr<bool>("trans_x");
+    bool transpose_y = ctx.Attr<bool>("trans_y");
 
+    if (transpose_x) {
+      if (transpose_y) {
+        ComputeImpl<true, true>(ctx);
+      } else {
+        ComputeImpl<true, false>(ctx);
+      }
+    } else {
+      if (transpose_y) {
+        ComputeImpl<false, true>(ctx);
+      } else {
+        ComputeImpl<false, false>(ctx);
+      }
+    }
+  }
+
+ private:
+  template <bool TransX, bool TransY>
+  static void ComputeImpl(const framework::ExecutionContext& ctx) {
+    using Trait = FusedGEMMGradTrait<TransX, TransY>;
+    auto& dev_ctx = ctx.template device_context<platform::CUDADeviceContext>();
     const Tensor* dout = ctx.Input<Tensor>("DOut");
     const Tensor* x = ctx.Input<Tensor>("X");
     const Tensor* y = ctx.Input<Tensor>("Y");
@@ -208,13 +294,18 @@ class FusedGemmEpilogueGradKernel : public framework::OpKernel<T> {
 
     std::string activation_grad = ctx.Attr<std::string>("activation_grad");
 
-    auto dout_mat_dims =
-        phi::flatten_to_2d(dout->dims(), dout->dims().size() - 1);
-    auto x_mat_dims = phi::flatten_to_2d(x->dims(), x->dims().size() - 1);
+    VLOG(10) << "trans_x = " << TransX << " , trans_y = " << TransY
+             << " , activation_grad = " << activation_grad;
+
+    auto x_mat_dims =
+        phi::flatten_to_2d(x->dims(), TransX ? 1 : x->dims().size() - 1);
+
+    // (M * K) * (K * N)
+    int64_t M = TransX ? x_mat_dims[1] : x_mat_dims[0];
+    int64_t K = TransY ? y->dims()[1] : y->dims()[0];
+    int64_t N = TransY ? y->dims()[0] : y->dims()[1];
 
-    int64_t M = x_mat_dims[0];
-    int64_t K = y->dims()[0];
-    int64_t N = y->dims()[1];
+    VLOG(10) << "M = " << M << " , K = " << K << " , N = " << N;
 
     cudaDataType_t mat_type = CUDA_R_32F;
     cudaDataType_t scale_type = CUDA_R_32F;
@@ -229,7 +320,8 @@ class FusedGemmEpilogueGradKernel : public framework::OpKernel<T> {
     }
 
     cublasLtHandle_t lt_handle = dev_ctx.cublaslt_handle();
-    size_t workspace_size = 4 * 1024 * 1024;
+    size_t workspace_size = static_cast<size_t>(4) * 1024 * 1024 * 1024;
+    const cublasLtMatmulAlgo_t* algo = nullptr;
     cudaStream_t stream = dev_ctx.stream();
 
     double alpha64 = 1.0, beta64 = 0.0;
@@ -243,24 +335,81 @@ class FusedGemmEpilogueGradKernel : public framework::OpKernel<T> {
       beta = &beta32;
     }
 
-    cublasOperation_t trans_dout = CUBLAS_OP_N;
-    cublasLtMatrixLayout_t dout_desc = NULL;
-    PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
-        &dout_desc, mat_type, N, M, N));
+    cublasLtMatrixLayout_t dout_desc = nullptr, dout_trans_desc = nullptr;
+    cublasLtMatrixLayout_t x_desc = nullptr, x_trans_desc = nullptr;
+    cublasLtMatrixLayout_t y_desc = nullptr, y_trans_desc = nullptr;
+    cublasLtMatrixLayout_t dx_desc = nullptr, dy_desc = nullptr;
+    cublasLtMatmulDesc_t dx_operation_desc = nullptr,
+                         dy_operation_desc = nullptr;
+
+    DEFINE_PADDLE_SCOPE_GUARD([&] {
+      auto descs = {dout_desc, dout_trans_desc, x_desc,  x_trans_desc,
+                    y_desc,    y_trans_desc,    dx_desc, dy_desc};
+      for (auto desc : descs) {
+        if (desc) {
+          PADDLE_ENFORCE_GPU_SUCCESS(
+              platform::dynload::cublasLtMatrixLayoutDestroy(desc));
+        }
+      }
 
+      if (dx_operation_desc) {
+        PADDLE_ENFORCE_GPU_SUCCESS(
+            platform::dynload::cublasLtMatmulDescDestroy(dx_operation_desc));
+      }
+
+      if (dy_operation_desc) {
+        PADDLE_ENFORCE_GPU_SUCCESS(
+            platform::dynload::cublasLtMatmulDescDestroy(dy_operation_desc));
+      }
+    });
+
+    auto x_row = TransX ? K : M;
+    auto x_col = TransX ? M : K;
+    auto y_row = TransY ? N : K;
+    auto y_col = TransY ? K : N;
+    auto z_row = TransX ? N : M;
+    auto z_col = TransX ? M : N;
+
+    // dx = func(dout, y)
     if (dx) {
-      cublasLtMatmulDesc_t dx_operation_desc = NULL;
+      constexpr auto kXGradAIsDZ = (Trait::kXGradA == FusedGEMMGradInType::kDZ);
+      cublasLtMatrixLayout_t *dx_dout_desc, *dx_y_desc;
+
+      if (TransX) {
+        dx_dout_desc = &dout_trans_desc;
+        PADDLE_ENFORCE_GPU_SUCCESS(
+            platform::dynload::cublasLtMatrixLayoutCreate(
+                dx_dout_desc, mat_type, z_row, z_col, z_row));
+      } else {
+        dx_dout_desc = &dout_desc;
+        PADDLE_ENFORCE_GPU_SUCCESS(
+            platform::dynload::cublasLtMatrixLayoutCreate(
+                dx_dout_desc, mat_type, z_col, z_row, z_col));
+      }
+
+      dx_y_desc = &y_trans_desc;
+      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
+          dx_y_desc, mat_type, y_col, y_row, y_col));
+
+      auto& a_desc = kXGradAIsDZ ? (*dx_dout_desc) : (*dx_y_desc);
+      auto& b_desc = kXGradAIsDZ ? (*dx_y_desc) : (*dx_dout_desc);
+      auto a_trans = BoolToCuBlasEnum(Trait::kXGradATrans);
+      auto b_trans = BoolToCuBlasEnum(Trait::kXGradBTrans);
+
+      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
+          &dx_desc, mat_type, x_col, x_row, x_col));
+
       PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatmulDescCreate(
           &dx_operation_desc, compute_type, scale_type));
-      cublasOperation_t trans_y = CUBLAS_OP_T;
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
-              dx_operation_desc, CUBLASLT_MATMUL_DESC_TRANSB, &trans_dout,
-              sizeof(trans_dout)));
+              dx_operation_desc, CUBLASLT_MATMUL_DESC_TRANSB, &a_trans,
+              sizeof(a_trans)));
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
-              dx_operation_desc, CUBLASLT_MATMUL_DESC_TRANSA, &trans_y,
-              sizeof(trans_y)));
+              dx_operation_desc, CUBLASLT_MATMUL_DESC_TRANSA, &b_trans,
+              sizeof(b_trans)));
+
       cublasLtEpilogue_t epiloque_func_for_dx =
           get_epilogue_type_(activation_grad);
       PADDLE_ENFORCE_GPU_SUCCESS(
@@ -274,105 +423,116 @@ class FusedGemmEpilogueGradKernel : public framework::OpKernel<T> {
             platform::dynload::cublasLtMatmulDescSetAttribute(
                 dx_operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_POINTER,
                 &aux_data, sizeof(aux_data)));
+        int64_t aux_ld = TransX ? M : K;
         PADDLE_ENFORCE_GPU_SUCCESS(
             platform::dynload::cublasLtMatmulDescSetAttribute(
-                dx_operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_LD, &K,
-                sizeof(K)));
+                dx_operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE_AUX_LD,
+                &aux_ld, sizeof(aux_ld)));
       }
 
-      cublasLtMatrixLayout_t y_desc = NULL, dx_desc = NULL;
-      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
-          &y_desc, mat_type, N, K, N));
-      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
-          &dx_desc, mat_type, K, M, K));
-
-      memory::allocation::AllocationPtr dx_workspace =
-          memory::Alloc(dev_ctx, workspace_size);
+      auto dx_workspace = memory::Alloc(dev_ctx, workspace_size);
 
-      dx->mutable_data<T>(ctx.GetPlace());
-      auto* dx_data = dx->data<T>();
+      auto* dx_data = dx->mutable_data<T>(ctx.GetPlace());
       const auto* y_data = y->data<T>();
       const auto* dout_data = dout->data<T>();
+      const auto* a_data = kXGradAIsDZ ? dout_data : y_data;
+      const auto* b_data = kXGradAIsDZ ? y_data : dout_data;
 
-      cublasLtMatmulAlgo_t algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
-          lt_handle, dx_operation_desc, y_desc, dout_desc, dx_desc, alpha, beta,
-          y_data, dout_data, dx_data, stream, dx_workspace->ptr(),
-          workspace_size);
+      auto algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
+          lt_handle, dx_operation_desc, b_desc, a_desc, dx_desc, alpha, beta,
+          b_data, a_data, dx_data, stream, dx_workspace->ptr(), workspace_size);
 
       PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatmul(
-          lt_handle, dx_operation_desc, alpha, y->data<T>(), y_desc,
-          dout->data<T>(), dout_desc, beta, dx_data, dx_desc, dx_data, dx_desc,
-          &algo, dx_workspace->ptr(), workspace_size, stream));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulDescDestroy(dx_operation_desc));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatrixLayoutDestroy(y_desc));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatrixLayoutDestroy(dx_desc));
+          lt_handle, dx_operation_desc, alpha, b_data, b_desc, a_data, a_desc,
+          beta, dx_data, dx_desc, dx_data, dx_desc, algo, dx_workspace->ptr(),
+          workspace_size, stream));
     }
 
+    // dy = func(dout, x)
     if (dy) {
-      cublasLtMatmulDesc_t dy_operation_desc = NULL;
+      constexpr auto kYGradAIsDZ = (Trait::kYGradA == FusedGEMMGradInType::kDZ);
+
+      cublasLtMatrixLayout_t *dy_dout_desc = nullptr, *dy_x_desc = nullptr;
+      if (TransX) {
+        dy_dout_desc = &dout_trans_desc;
+        if (dout_trans_desc == nullptr) {
+          PADDLE_ENFORCE_GPU_SUCCESS(
+              platform::dynload::cublasLtMatrixLayoutCreate(
+                  dy_dout_desc, mat_type, z_row, z_col, z_row));
+        }
+      } else {
+        dy_dout_desc = &dout_desc;
+        if (dout_desc == nullptr) {
+          PADDLE_ENFORCE_GPU_SUCCESS(
+              platform::dynload::cublasLtMatrixLayoutCreate(
+                  dy_dout_desc, mat_type, z_col, z_row, z_col));
+        }
+      }
+
+      dy_x_desc = &x_trans_desc;
+      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
+          dy_x_desc, mat_type, x_col, x_row, x_col));
+
+      auto& a_desc = kYGradAIsDZ ? (*dy_dout_desc) : (*dy_x_desc);
+      auto& b_desc = kYGradAIsDZ ? (*dy_x_desc) : (*dy_dout_desc);
+      auto a_trans = BoolToCuBlasEnum(Trait::kYGradATrans);
+      auto b_trans = BoolToCuBlasEnum(Trait::kYGradBTrans);
+
+      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
+          &dy_desc, mat_type, y_col, y_row, y_col));
+
       PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatmulDescCreate(
           &dy_operation_desc, compute_type, scale_type));
-      cublasOperation_t trans_x = CUBLAS_OP_T;
+
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
-              dy_operation_desc, CUBLASLT_MATMUL_DESC_TRANSA, &trans_dout,
-              sizeof(trans_dout)));
+              dy_operation_desc, CUBLASLT_MATMUL_DESC_TRANSB, &a_trans,
+              sizeof(a_trans)));
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
-              dy_operation_desc, CUBLASLT_MATMUL_DESC_TRANSB, &trans_x,
-              sizeof(trans_x)));
-      cublasLtEpilogue_t epiloque_func_for_dy = dbias == nullptr
-                                                    ? CUBLASLT_EPILOGUE_DEFAULT
-                                                    : CUBLASLT_EPILOGUE_BGRADA;
+              dy_operation_desc, CUBLASLT_MATMUL_DESC_TRANSA, &b_trans,
+              sizeof(b_trans)));
+
+      cublasLtEpilogue_t epiloque_func_for_dy;
+      if (dbias == nullptr) {
+        epiloque_func_for_dy = CUBLASLT_EPILOGUE_DEFAULT;
+      } else {
+        if (TransY) {
+          epiloque_func_for_dy = CUBLASLT_EPILOGUE_BGRADB;
+        } else {
+          epiloque_func_for_dy = CUBLASLT_EPILOGUE_BGRADA;
+        }
+      }
+
       PADDLE_ENFORCE_GPU_SUCCESS(
           platform::dynload::cublasLtMatmulDescSetAttribute(
               dy_operation_desc, CUBLASLT_MATMUL_DESC_EPILOGUE,
               &epiloque_func_for_dy, sizeof(epiloque_func_for_dy)));
 
       if (dbias) {
-        dbias->mutable_data<T>(ctx.GetPlace());
-        auto* dbias_data = dbias->data<T>();
+        auto* dbias_data = dbias->mutable_data<T>(ctx.GetPlace());
         PADDLE_ENFORCE_GPU_SUCCESS(
             platform::dynload::cublasLtMatmulDescSetAttribute(
                 dy_operation_desc, CUBLASLT_MATMUL_DESC_BIAS_POINTER,
                 &dbias_data, sizeof(dbias_data)));
       }
 
-      cublasLtMatrixLayout_t x_desc = NULL, dy_desc = NULL;
-      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
-          &x_desc, mat_type, K, M, K));
-      PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatrixLayoutCreate(
-          &dy_desc, mat_type, N, K, N));
-
-      memory::allocation::AllocationPtr dy_workspace =
-          memory::Alloc(dev_ctx, workspace_size);
-
-      dy->mutable_data<T>(ctx.GetPlace());
-      auto* dy_data = dy->data<T>();
+      auto dy_workspace = memory::Alloc(dev_ctx, workspace_size);
+      auto* dy_data = dy->mutable_data<T>(ctx.GetPlace());
       const auto* dout_data = dout->data<T>();
       const auto* x_data = x->data<T>();
+      const auto* a_data = kYGradAIsDZ ? dout_data : x_data;
+      const auto* b_data = kYGradAIsDZ ? x_data : dout_data;
 
-      cublasLtMatmulAlgo_t algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
-          lt_handle, dy_operation_desc, dout_desc, x_desc, dy_desc, alpha, beta,
-          dout_data, x_data, dy_data, stream, dy_workspace->ptr(),
-          workspace_size);
+      auto algo = GemmEpilogueAlgoCache::Instance().GetGemmAlgo(
+          lt_handle, dy_operation_desc, b_desc, a_desc, dy_desc, alpha, beta,
+          b_data, a_data, dy_data, stream, dy_workspace->ptr(), workspace_size);
 
       PADDLE_ENFORCE_GPU_SUCCESS(platform::dynload::cublasLtMatmul(
-          lt_handle, dy_operation_desc, alpha, dout_data, dout_desc, x_data,
-          x_desc, beta, dy_data, dy_desc, dy_data, dy_desc, &algo,
-          dy_workspace->ptr(), workspace_size, stream));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulDescDestroy(dy_operation_desc));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatrixLayoutDestroy(x_desc));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatrixLayoutDestroy(dy_desc));
+          lt_handle, dy_operation_desc, alpha, b_data, b_desc, a_data, a_desc,
+          beta, dy_data, dy_desc, dy_data, dy_desc, algo, dy_workspace->ptr(),
+          workspace_size, stream));
     }
-    PADDLE_ENFORCE_GPU_SUCCESS(
-        platform::dynload::cublasLtMatrixLayoutDestroy(dout_desc));
   }
 
  private:
diff --git a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.h b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.h
index c90a6966fe0a841dd3eb692aaafcdd03535b16a0..8ff41b2c9616bbda80bf9be7fd3e8d9556560c86 100644
--- a/paddle/fluid/operators/fused/fused_gemm_epilogue_op.h
+++ b/paddle/fluid/operators/fused/fused_gemm_epilogue_op.h
@@ -21,7 +21,9 @@ limitations under the License. */
 #include <unordered_map>
 #include "gflags/gflags.h"
 #include "paddle/fluid/platform/dynload/cublasLt.h"
+#include "paddle/fluid/platform/enforce.h"
 #include "paddle/fluid/platform/float16.h"
+#include "paddle/utils/optional.h"
 
 DECLARE_int64(cublaslt_exhaustive_search_times);
 
@@ -39,12 +41,14 @@ class GemmEpilogueAlgoCache {
   GemmEpilogueAlgoCache(GemmEpilogueAlgoCache const &) = delete;
   void operator=(GemmEpilogueAlgoCache const &) = delete;
 
-  cublasLtMatmulAlgo_t GetGemmAlgo(
+  cublasLtMatmulAlgo_t *GetGemmAlgo(
       cublasLtHandle_t lt_handle, cublasLtMatmulDesc_t op_desc,
       cublasLtMatrixLayout_t a_desc, cublasLtMatrixLayout_t b_desc,
       cublasLtMatrixLayout_t c_desc, const void *alpha, const void *beta,
       const void *a, const void *b, void *c, cudaStream_t stream,
       void *workspace, size_t workspace_size) {
+    if (search_times_ <= 0) return nullptr;
+
     int64_t seed = 0;
     std::hash<int64_t> hash_fn;
 
@@ -54,132 +58,108 @@ class GemmEpilogueAlgoCache {
     HashMatrixLayoutDesc_(c_desc, &seed, hash_fn);
 
     cublasLtMatmulAlgo_t ret;
-    auto it = map_.end();
-    bool have_found = false;
     {
       std::lock_guard<std::mutex> lock(cache_mutex_);
-      it = map_.find(seed);
-
+      auto it = map_.find(seed);
       if (it != map_.end()) {
-        ret = it->second;
-        have_found = true;
+        return &(it->second);
       }
     }
 
-    if (!have_found) {
-      cublasLtMatmulPreference_t preference;
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulPreferenceCreate(&preference));
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulPreferenceSetAttribute(
-              preference, CUBLASLT_MATMUL_PREF_MAX_WORKSPACE_BYTES,
-              &workspace_size, sizeof(workspace_size)));
-
-      int returned_results = 0;
-      cublasLtMatmulHeuristicResult_t heuristic_results[requested_algo_count_] =
-          {0};
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulAlgoGetHeuristic(
-              lt_handle, op_desc, a_desc, b_desc, c_desc, c_desc, preference,
-              requested_algo_count_, heuristic_results, &returned_results));
-
-      PADDLE_ENFORCE_GT(
-          returned_results, 0,
-          platform::errors::Unavailable("No GEMM epilogue algorithm support!"));
-
-      PADDLE_ENFORCE_GPU_SUCCESS(
-          platform::dynload::cublasLtMatmulPreferenceDestroy(preference));
-
-      if (search_times_ > 0) {
-        int best_algo_idx = -1;
-        float best_algo_time = 0;
-
-        // Run 100 times for warmup
-        int warmup_algo_idx = 0;
-        for (int t = 0; t < 100; t++) {
-          cublasStatus_t status = platform::dynload::cublasLtMatmul(
-              lt_handle, op_desc, alpha, a, a_desc, b, b_desc, beta, c, c_desc,
-              c, c_desc, &heuristic_results[warmup_algo_idx].algo, workspace,
-              workspace_size, stream);
-          if (status != CUBLAS_STATUS_SUCCESS) {
-            t = -1;
-            warmup_algo_idx += 1;
-            if (warmup_algo_idx == requested_algo_count_) {
-              PADDLE_THROW(platform::errors::Unavailable(
-                  "No GEMM epilogue algorithm support!"));
-            }
-          }
-        }
+    cublasLtMatmulPreference_t preference;
+    PADDLE_ENFORCE_GPU_SUCCESS(
+        platform::dynload::cublasLtMatmulPreferenceCreate(&preference));
+    PADDLE_ENFORCE_GPU_SUCCESS(
+        platform::dynload::cublasLtMatmulPreferenceSetAttribute(
+            preference, CUBLASLT_MATMUL_PREF_MAX_WORKSPACE_BYTES,
+            &workspace_size, sizeof(workspace_size)));
 
-        cudaEvent_t start_event, stop_event;
-        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventCreate(&start_event));
-        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventCreate(&stop_event));
-
-        for (int algo_idx = 0; algo_idx < returned_results; ++algo_idx) {
-          float curr_time = 0;
-          for (int check_idx = 0; check_idx < search_times_; check_idx++) {
-            float time = 0;
-            PADDLE_ENFORCE_GPU_SUCCESS(cudaEventRecord(start_event, stream));
-
-            cublasStatus_t status = platform::dynload::cublasLtMatmul(
-                lt_handle, op_desc, alpha, a, a_desc, b, b_desc, beta, c,
-                c_desc, c, c_desc, &heuristic_results[algo_idx].algo, workspace,
-                workspace_size, stream);
-
-            PADDLE_ENFORCE_GPU_SUCCESS(cudaEventRecord(stop_event, stream));
-            PADDLE_ENFORCE_GPU_SUCCESS(cudaEventSynchronize(stop_event));
-            PADDLE_ENFORCE_GPU_SUCCESS(
-                cudaEventElapsedTime(&time, start_event, stop_event));
-            curr_time += time;
-            if (status != CUBLAS_STATUS_SUCCESS) {
-              curr_time = 3.40282e+038;  // Max Value of float
-              break;
-            }
-          }
-
-          curr_time = curr_time / search_times_;
-          if (curr_time < best_algo_time || algo_idx == 0) {
-            best_algo_idx = algo_idx;
-            best_algo_time = curr_time;
-          }
-        }
+    int returned_results = 0;
+    std::vector<cublasLtMatmulHeuristicResult_t> heuristic_results(
+        requested_algo_count_);
+    PADDLE_ENFORCE_GPU_SUCCESS(
+        platform::dynload::cublasLtMatmulAlgoGetHeuristic(
+            lt_handle, op_desc, a_desc, b_desc, c_desc, c_desc, preference,
+            requested_algo_count_, heuristic_results.data(),
+            &returned_results));
 
-        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventDestroy(start_event));
-        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventDestroy(stop_event));
+    PADDLE_ENFORCE_GT(
+        returned_results, 0,
+        platform::errors::Unavailable("No GEMM epilogue algorithm support!"));
 
-        if (best_algo_idx == -1) {
+    PADDLE_ENFORCE_GPU_SUCCESS(
+        platform::dynload::cublasLtMatmulPreferenceDestroy(preference));
+
+    int best_algo_idx = -1;
+    float best_algo_time = 0;
+
+    // Run 100 times for warmup
+    int warmup_algo_idx = 0;
+    for (int t = 0; t < 100; t++) {
+      cublasStatus_t status = platform::dynload::cublasLtMatmul(
+          lt_handle, op_desc, alpha, a, a_desc, b, b_desc, beta, c, c_desc, c,
+          c_desc, &heuristic_results[warmup_algo_idx].algo, workspace,
+          workspace_size, stream);
+      if (status != CUBLAS_STATUS_SUCCESS) {
+        t = -1;
+        warmup_algo_idx += 1;
+        if (warmup_algo_idx == requested_algo_count_) {
           PADDLE_THROW(platform::errors::Unavailable(
               "No GEMM epilogue algorithm support!"));
         }
+      }
+    }
 
-        ret = heuristic_results[best_algo_idx].algo;
-      } else {
-        int decided_algo_idx = -1;
-        for (int algo_idx = 0; algo_idx < returned_results; ++algo_idx) {
-          cublasStatus_t status = platform::dynload::cublasLtMatmul(
-              lt_handle, op_desc, alpha, a, a_desc, b, b_desc, beta, c, c_desc,
-              c, c_desc, &heuristic_results[algo_idx].algo, workspace,
-              workspace_size, stream);
-          if (status == CUBLAS_STATUS_SUCCESS) {
-            decided_algo_idx = algo_idx;
-            break;
-          }
-        }
-        if (decided_algo_idx == -1) {
-          PADDLE_THROW(platform::errors::Unavailable(
-              "No GEMM epilogue algorithm support!"));
+    cudaEvent_t start_event, stop_event;
+    PADDLE_ENFORCE_GPU_SUCCESS(cudaEventCreate(&start_event));
+    PADDLE_ENFORCE_GPU_SUCCESS(cudaEventCreate(&stop_event));
+
+    for (int algo_idx = 0; algo_idx < returned_results; ++algo_idx) {
+      float curr_time = 0;
+      for (int check_idx = 0; check_idx < search_times_; check_idx++) {
+        float time = 0;
+        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventRecord(start_event, stream));
+
+        cublasStatus_t status = platform::dynload::cublasLtMatmul(
+            lt_handle, op_desc, alpha, a, a_desc, b, b_desc, beta, c, c_desc, c,
+            c_desc, &heuristic_results[algo_idx].algo, workspace,
+            workspace_size, stream);
+
+        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventRecord(stop_event, stream));
+        PADDLE_ENFORCE_GPU_SUCCESS(cudaEventSynchronize(stop_event));
+        PADDLE_ENFORCE_GPU_SUCCESS(
+            cudaEventElapsedTime(&time, start_event, stop_event));
+        curr_time += time;
+        if (status != CUBLAS_STATUS_SUCCESS) {
+          curr_time = 3.40282e+038;  // Max Value of float
+          break;
         }
-        ret = heuristic_results[decided_algo_idx].algo;
       }
 
-      std::lock_guard<std::mutex> lock(cache_mutex_);
-      map_[seed] = ret;
+      curr_time = curr_time / search_times_;
+      if (curr_time < best_algo_time || algo_idx == 0) {
+        best_algo_idx = algo_idx;
+        best_algo_time = curr_time;
+      }
     }
 
-    VLOG(4) << "Search time:" << search_times_ << ", Is hash-key (" << seed
-            << ") found in GemmEpilogueAlgoCache? " << have_found;
+    PADDLE_ENFORCE_GPU_SUCCESS(cudaEventDestroy(start_event));
+    PADDLE_ENFORCE_GPU_SUCCESS(cudaEventDestroy(stop_event));
+
+    if (best_algo_idx == -1) {
+      PADDLE_THROW(
+          platform::errors::Unavailable("No GEMM epilogue algorithm support!"));
+    }
+
+    ret = heuristic_results[best_algo_idx].algo;
+
+    VLOG(4) << "Search time:" << search_times_ << ", hash-key (" << seed
+            << ") not found in GemmEpilogueAlgoCache";
 
-    return ret;
+    std::lock_guard<std::mutex> lock(cache_mutex_);
+    auto &algo_in_map = map_[seed];
+    algo_in_map = ret;
+    return &algo_in_map;
   }
 
  private:
diff --git a/python/paddle/fluid/ir.py b/python/paddle/fluid/ir.py
index 55297ed516ffb4f2e64abb44030b642785f03cbd..2756eac990ed328134c87808cb2a08137e829d86 100644
--- a/python/paddle/fluid/ir.py
+++ b/python/paddle/fluid/ir.py
@@ -101,6 +101,9 @@ def apply_build_strategy(main_program, startup_program, build_strategy,
     if build_strategy.enable_auto_fusion and use_cuda:
         apply_pass("fusion_group_pass")
         build_strategy.enable_auto_fusion = False
+    if build_strategy.fuse_gemm_epilogue:
+        apply_pass("fuse_gemm_epilogue_pass")
+        build_strategy.fuse_gemm_epilogue = False
     if build_strategy.fuse_elewise_add_act_ops:
         apply_pass("fuse_elewise_add_act_pass")
         build_strategy.fuse_elewise_add_act_ops = False
diff --git a/python/paddle/fluid/tests/unittests/op_test.py b/python/paddle/fluid/tests/unittests/op_test.py
index f7a3dfa1102b295096662f71d965e6aa48406a5a..fe1dbf3b92743d364e11e09d57142f2c5300289f 100644
--- a/python/paddle/fluid/tests/unittests/op_test.py
+++ b/python/paddle/fluid/tests/unittests/op_test.py
@@ -263,6 +263,18 @@ def skip_check_grad_ci(reason=None):
     return wrapper
 
 
+def skip_check_inplace_ci(reason=None):
+    if not isinstance(reason, str):
+        raise AssertionError(
+            "The reason for skipping check_inplace is required.")
+
+    def wrapper(cls):
+        cls.no_need_check_inplace = True
+        return cls
+
+    return wrapper
+
+
 def copy_bits_from_float_to_uint16(f):
     return struct.unpack('<I', struct.pack('<f', f))[0] >> 16
 
@@ -1288,6 +1300,9 @@ class OpTest(unittest.TestCase):
         Returns:
             None
         """
+        if getattr(self, "no_need_check_inplace", False):
+            return
+
         has_infer_inplace = fluid.core.has_infer_inplace(self.op_type)
         has_grad_op_maker = fluid.core.has_grad_op_maker(self.op_type)
 
diff --git a/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_grad_op.py b/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_grad_op.py
index 2ea1bf2e9cb8105280a4f2635279518d125a4312..106ce5b4ef055311a5ba511c0c0b90612e410fbe 100644
--- a/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_grad_op.py
+++ b/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_grad_op.py
@@ -235,5 +235,6 @@ class TestFuseGemmEpilogueGradOpDXYFP64(TestFuseGemmEpilogueGradOpDXYFP16):
 
 
 if __name__ == "__main__":
+    paddle.enable_static()
     np.random.seed(0)
     unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_op.py b/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_op.py
index f826898f9e5dd601b54eaeb1c54216414a70246b..4256945a1e8d572f35cdabb1579bc8ffbfc38644 100644
--- a/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_op.py
+++ b/python/paddle/fluid/tests/unittests/test_fused_gemm_epilogue_op.py
@@ -19,7 +19,7 @@ import unittest
 import numpy as np
 import paddle
 import paddle.fluid.core as core
-from op_test import OpTest, skip_check_grad_ci
+from op_test import OpTest, skip_check_grad_ci, skip_check_inplace_ci
 
 
 def gelu(x):
@@ -43,10 +43,15 @@ def get_output(X, Y, bias, act):
         return out
 
 
+@skip_check_inplace_ci(reason="no inplace op")
+class TestFuseGemmBase(OpTest):
+    pass
+
+
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMMFP16(OpTest):
+class TestFuseGemmEpilogueOpReluMMFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -95,7 +100,7 @@ class TestFuseGemmEpilogueOpReluMMFP64(TestFuseGemmEpilogueOpReluMMFP16):
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMTMFP16(OpTest):
+class TestFuseGemmEpilogueOpReluMTMFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -144,7 +149,7 @@ class TestFuseGemmEpilogueOpReluMTMFP64(TestFuseGemmEpilogueOpReluMTMFP16):
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMMTFP16(OpTest):
+class TestFuseGemmEpilogueOpReluMMTFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -193,7 +198,7 @@ class TestFuseGemmEpilogueOpReluMMTFP64(TestFuseGemmEpilogueOpReluMMTFP16):
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMTMTFP16(OpTest):
+class TestFuseGemmEpilogueOpReluMTMTFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -242,7 +247,7 @@ class TestFuseGemmEpilogueOpReluMTMTFP64(TestFuseGemmEpilogueOpReluMTMTFP16):
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMMFP16MultiDimX(OpTest):
+class TestFuseGemmEpilogueOpReluMMFP16MultiDimX(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -294,7 +299,7 @@ class TestFuseGemmEpilogueOpReluMMFP64MultiDimX(
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpReluMTMFP16MultiDimX(OpTest):
+class TestFuseGemmEpilogueOpReluMTMFP16MultiDimX(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -346,7 +351,7 @@ class TestFuseGemmEpilogueOpReluMTMFP64MultiDimX(
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpGeluMMFP16(OpTest):
+class TestFuseGemmEpilogueOpGeluMMFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -397,7 +402,7 @@ class TestFuseGemmEpilogueOpGeluMMFP64(TestFuseGemmEpilogueOpGeluMMFP16):
 @skip_check_grad_ci(reason="no grap op")
 @unittest.skipIf(not core.is_compiled_with_cuda(),
                  "core is not compiled with CUDA")
-class TestFuseGemmEpilogueOpNoneMMFP16(OpTest):
+class TestFuseGemmEpilogueOpNoneMMFP16(TestFuseGemmBase):
     def setUp(self):
         self.op_type = "fused_gemm_epilogue"
         self.place = core.CUDAPlace(0)
@@ -446,5 +451,6 @@ class TestFuseGemmEpilogueOpNoneMMFP64(TestFuseGemmEpilogueOpNoneMMFP16):
 
 
 if __name__ == "__main__":
+    paddle.enable_static()
     np.random.seed(0)
     unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_fused_matmul_bias.py b/python/paddle/fluid/tests/unittests/test_fused_matmul_bias.py
new file mode 100644
index 0000000000000000000000000000000000000000..98548c9996588938a96d431b11cd9443d3f968ae
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_fused_matmul_bias.py
@@ -0,0 +1,162 @@
+# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import paddle
+import paddle.fluid.core as core
+import unittest
+import numpy as np
+from paddle.incubate.nn.functional import fused_matmul_bias, fused_linear
+from paddle.incubate.nn import FusedLinear
+
+
+def is_fused_matmul_bias_supported():
+    if paddle.is_compiled_with_cuda() and not paddle.is_compiled_with_rocm():
+        return hasattr(core.ops, 'fused_gemm_epilogue')
+    else:
+        return False
+
+
+def matmul(x, y, bias, trans_x, trans_y):
+    x = np.array(x)
+    if trans_x:
+        x = np.ascontiguousarray(np.transpose(x))
+    if trans_y:
+        y = np.ascontiguousarray(np.transpose(y))
+    z = np.matmul(x, y)
+    if bias is None:
+        return z
+    else:
+        return z + bias
+
+
+def matmul_grad(x, y, bias, dz, trans_x, trans_y):
+    if trans_x:
+        if trans_y:
+            dx = matmul(y, dz, None, True, True)
+            dy = matmul(dz, x, None, True, True)
+        else:
+            dx = matmul(y, dz, None, False, True)
+            dy = matmul(x, dz, None, False, False)
+    else:
+        if trans_y:
+            dx = matmul(dz, y, None, False, False)
+            dy = matmul(dz, x, None, True, False)
+        else:
+            dx = matmul(dz, y, None, False, True)
+            dy = matmul(x, dz, None, True, False)
+    if bias is None:
+        dbias = None
+    else:
+        dbias = np.sum(dz, axis=0, keepdims=False)
+    return dx, dy, dbias
+
+
+@unittest.skipIf(
+    not is_fused_matmul_bias_supported(),
+    "fused_gemm_epilogue is only supported when CUDA version >= 11.6")
+class TestFusedMatmulBias(unittest.TestCase):
+    def setUp(self):
+        paddle.set_device('gpu')
+
+    def rand_data(self, shape, dtype):
+        return np.random.randint(low=-20, high=20, size=shape).astype(dtype)
+
+    def rand_test_base(self, m, n, k, trans_x, trans_y, need_bias, dtype, seed):
+        np.random.seed(seed)
+        x_shape = [k, m] if trans_x else [m, k]
+        y_shape = [n, k] if trans_y else [k, n]
+        bias_shape = [n]
+
+        x_np = self.rand_data(x_shape, dtype)
+        x = paddle.to_tensor(x_np)
+        x.stop_gradient = False
+
+        y_np = self.rand_data(y_shape, dtype)
+        y = paddle.to_tensor(y_np)
+        y.stop_gradient = False
+
+        if need_bias:
+            bias_np = self.rand_data(bias_shape, dtype)
+            bias = paddle.to_tensor(bias_np)
+            bias.stop_gradient = False
+        else:
+            bias_np = None
+            bias = None
+
+        z = fused_matmul_bias(x, y, bias, trans_x, trans_y)
+        z_np = matmul(x_np, y_np, bias_np, trans_x, trans_y)
+        self.assertTrue(np.array_equal(z.numpy(), z_np))
+
+        z_grad_np = self.rand_data(z_np.shape, dtype)
+        paddle.autograd.backward(z, grad_tensors=[paddle.to_tensor(z_grad_np)])
+
+        x_grad_np, y_grad_np, bias_grad_np = matmul_grad(
+            x_np, y_np, bias_np, z_grad_np, trans_x, trans_y)
+        self.assertTrue(np.array_equal(x.grad.numpy(), x_grad_np))
+        self.assertEqual(y_grad_np.shape, y_np.shape)
+        self.assertTrue(np.array_equal(y.grad.numpy(), y_grad_np))
+
+        if need_bias:
+            self.assertTrue(np.array_equal(bias.grad.numpy(), bias_grad_np))
+        else:
+            self.assertTrue(bias_grad_np is None)
+
+    def rand_test(self, m, n, k, dtype):
+        seed = int(np.random.randint(low=0, high=1000, size=[1]))
+        for trans_x in [False, True]:
+            for trans_y in [False, True]:
+                for need_bias in [False, True]:
+                    self.rand_test_base(m, n, k, trans_x, trans_y, need_bias,
+                                        dtype, seed)
+
+    def test_fp32(self):
+        self.rand_test(30, 40, 50, np.float32)
+
+    def test_fp16(self):
+        self.rand_test(4, 5, 7, np.float16)
+
+
+@unittest.skipIf(
+    not is_fused_matmul_bias_supported(),
+    "fused_gemm_epilogue is only supported when CUDA version >= 11.6")
+class TestFusedLinear(unittest.TestCase):
+    def check_fused_linear(self, transpose):
+        x = paddle.randn([30, 40])
+        linear = FusedLinear(40, 50, transpose_weight=transpose)
+        y1 = linear(x)
+        y2 = fused_linear(x, linear.weight, linear.bias, transpose)
+        self.assertTrue(np.array_equal(y1.numpy(), y2.numpy()))
+
+    def test_non_transpose(self):
+        self.check_fused_linear(False)
+
+    def test_transpose(self):
+        self.check_fused_linear(True)
+
+
+@unittest.skipIf(
+    not is_fused_matmul_bias_supported(),
+    "fused_gemm_epilogue is only supported when CUDA version >= 11.6")
+class TestStaticGraph(unittest.TestCase):
+    def test_static_graph(self):
+        paddle.enable_static()
+        x = paddle.static.data(name='x', dtype='float32', shape=[-1, 100])
+        linear = FusedLinear(100, 300)
+        y = linear(x)
+        self.assertEqual(list(y.shape), [-1, 300])
+        paddle.disable_static()
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/python/paddle/incubate/nn/__init__.py b/python/paddle/incubate/nn/__init__.py
index 3c806aa646ebe3157ab06819c12829806f502aa0..cf15ee7d8ffaa321b2700c38b2dbea8682ad0a3f 100644
--- a/python/paddle/incubate/nn/__init__.py
+++ b/python/paddle/incubate/nn/__init__.py
@@ -16,6 +16,7 @@ from .layer.fused_transformer import FusedMultiHeadAttention  # noqa: F401
 from .layer.fused_transformer import FusedFeedForward  # noqa: F401
 from .layer.fused_transformer import FusedTransformerEncoderLayer  # noqa: F401
 from .layer.fused_transformer import FusedMultiTransformer  # noqa: F401
+from .layer.fused_linear import FusedLinear  # noqa: F401
 from .layer.fused_transformer import FusedBiasDropoutResidualLayerNorm  # noqa: F401
 
 __all__ = [  #noqa
@@ -23,5 +24,6 @@ __all__ = [  #noqa
     'FusedFeedForward',
     'FusedTransformerEncoderLayer',
     'FusedMultiTransformer',
+    'FusedLinear',
     'FusedBiasDropoutResidualLayerNorm',
 ]
diff --git a/python/paddle/incubate/nn/functional/__init__.py b/python/paddle/incubate/nn/functional/__init__.py
index 02e44548ce5d87a4be505dc6a2981405ee3cc938..e9894990455abf65972457ce67cdfeb164711b2c 100644
--- a/python/paddle/incubate/nn/functional/__init__.py
+++ b/python/paddle/incubate/nn/functional/__init__.py
@@ -15,11 +15,14 @@
 from .fused_transformer import fused_multi_head_attention
 from .fused_transformer import fused_feedforward
 from .fused_transformer import fused_multi_transformer
+from .fused_matmul_bias import fused_matmul_bias, fused_linear
 from .fused_transformer import fused_bias_dropout_residual_layer_norm
 
 __all__ = [
     'fused_multi_head_attention',
     'fused_feedforward',
     'fused_multi_transformer',
+    'fused_matmul_bias',
+    'fused_linear',
     'fused_bias_dropout_residual_layer_norm',
 ]
diff --git a/python/paddle/incubate/nn/functional/fused_matmul_bias.py b/python/paddle/incubate/nn/functional/fused_matmul_bias.py
new file mode 100644
index 0000000000000000000000000000000000000000..bcc2e62144589164779b7f927742e72ae0ee770d
--- /dev/null
+++ b/python/paddle/incubate/nn/functional/fused_matmul_bias.py
@@ -0,0 +1,105 @@
+# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from paddle.fluid.layer_helper import LayerHelper
+from paddle.fluid.framework import _non_static_mode
+from paddle.tensor.linalg import matmul
+from paddle import _C_ops
+
+
+def fused_matmul_bias(x,
+                      y,
+                      bias=None,
+                      transpose_x=False,
+                      transpose_y=False,
+                      name=None):
+    """
+    Applies matrix multiplication of two tensors and then bias addition if provided.
+    This method requires CUDA version >= 11.6. 
+
+    Args:
+        x (Tensor): the first input Tensor to be multiplied.
+        y (Tensor): the second input Tensor to be multiplied. Its rank must be 2.  
+        bias (Tensor|None): the input bias Tensor. If it is None, no bias addition would
+            be performed. Otherwise, the bias is added to the matrix multiplication result.  
+        transpose_x (bool): Whether to transpose :math:`x` before multiplication.
+        transpose_y (bool): Whether to transpose :math:`y` before multiplication.    
+        name(str|None): For detailed information, please refer to 
+            :ref:`api_guide_Name` . Usually name is no need to set and None by default. 
+
+    Returns:
+        Tensor: the output Tensor. 
+
+    Examples:
+        .. code-block:: python
+
+            # required: gpu
+            import paddle
+            from paddle.incubate.nn.functional import fused_matmul_bias
+            
+            x = paddle.randn([3, 4]) 
+            y = paddle.randn([4, 5])
+            bias = paddle.randn([5])
+            out = fused_matmul_bias(x, y, bias) 
+            print(out.shape) # [3, 5]
+    """
+    if bias is None:
+        return matmul(x, y, transpose_x, transpose_y, name)
+    if _non_static_mode():
+        return _C_ops.fused_gemm_epilogue(x, y, bias, 'trans_x', transpose_x,
+                                          'trans_y', transpose_y)
+
+    helper = LayerHelper('fused_matmul_bias', **locals())
+    out = helper.create_variable_for_type_inference(dtype=x.dtype)
+    helper.append_op(
+        type='fused_gemm_epilogue',
+        inputs={'X': x,
+                'Y': y,
+                'Bias': bias},
+        outputs={'Out': out},
+        attrs={'trans_x': transpose_x,
+               'trans_y': transpose_y})
+    return out
+
+
+def fused_linear(x, weight, bias=None, transpose_weight=False, name=None):
+    """
+    Fully-connected linear transformation operator. This method requires CUDA version >= 11.6. 
+
+    Args:
+        x (Tensor): the input Tensor to be multiplied.
+        weight (Tensor): the weight Tensor to be multiplied. Its rank must be 2.  
+        bias (Tensor|None): the input bias Tensor. If it is None, no bias addition would
+            be performed. Otherwise, the bias is added to the matrix multiplication result.  
+        transpose_weight (bool): Whether to transpose :math:`weight` before multiplication.    
+        name(str|None): For detailed information, please refer to 
+            :ref:`api_guide_Name` . Usually name is no need to set and None by default. 
+
+    Returns:
+        Tensor: the output Tensor. 
+
+    Examples:
+        .. code-block:: python
+
+            # required: gpu
+            import paddle
+            from paddle.incubate.nn.functional import fused_linear
+            
+            x = paddle.randn([3, 4]) 
+            weight = paddle.randn([4, 5])
+            bias = paddle.randn([5])
+            out = fused_linear(x, weight, bias) 
+            print(out.shape) # [3, 5]
+    """
+    return fused_matmul_bias(x, weight, bias, False, transpose_weight, name)
diff --git a/python/paddle/incubate/nn/layer/fused_linear.py b/python/paddle/incubate/nn/layer/fused_linear.py
new file mode 100644
index 0000000000000000000000000000000000000000..f7c872c3993cf747d302394129186d9f2cc779f5
--- /dev/null
+++ b/python/paddle/incubate/nn/layer/fused_linear.py
@@ -0,0 +1,91 @@
+# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from paddle.nn import Layer
+from paddle.incubate.nn import functional as F
+
+
+class FusedLinear(Layer):
+    """
+    Linear layer takes only one multi-dimensional tensor as input with the
+    shape :math:`[batch\_size, *, in\_features]` , where :math:`*` means any
+    number of additional dimensions. It multiplies input tensor with the weight
+    (a 2-D tensor of shape :math:`[in\_features, out\_features]` ) and produces
+    an output tensor of shape :math:`[batch\_size, *, out\_features]` .
+    If :math:`bias\_attr` is not False, the bias (a 1-D tensor of
+    shape :math:`[out\_features]` ) will be created and added to the output.
+
+    Parameters:
+        in_features (int): The number of input units.
+        out_features (int): The number of output units.
+        weight_attr (ParamAttr, optional): The attribute for the learnable
+            weight of this layer. The default value is None and the weight will be
+            initialized to zero. For detailed information, please refer to
+            paddle.ParamAttr.
+        transpose_weight (bool): Whether to transpose the `weight` Tensor before
+            multiplication. 
+        bias_attr (ParamAttr|bool, optional): The attribute for the learnable bias
+            of this layer. If it is set to False, no bias will be added to the output.
+            If it is set to None or one kind of ParamAttr, a bias parameter will
+            be created according to ParamAttr. For detailed information, please refer
+            to paddle.ParamAttr. The default value is None and the bias will be
+            initialized to zero.
+        name (str, optional): Normally there is no need for user to set this parameter.
+            For detailed information, please refer to :ref:`api_guide_Name` .
+
+    Attribute:
+        **weight** (Parameter): the learnable weight of this layer.
+
+        **bias** (Parameter): the learnable bias of this layer.
+
+    Shape:
+        - input: Multi-dimentional tensor with shape :math:`[batch\_size, *, in\_features]` .
+        - output: Multi-dimentional tensor with shape :math:`[batch\_size, *, out\_features]` .
+
+    Examples:
+        .. code-block:: python
+       
+            # required: gpu
+            import paddle
+            from paddle.incubate.nn import FusedLinear
+
+            x = paddle.randn([3, 4]) 
+            linear = FusedLinear(4, 5)
+            y = linear(x)            
+            print(y.shape) # [3, 5]
+    """
+
+    def __init__(self,
+                 in_features,
+                 out_features,
+                 weight_attr=None,
+                 bias_attr=None,
+                 transpose_weight=False,
+                 name=None):
+        super(FusedLinear, self).__init__()
+        if transpose_weight:
+            weight_shape = [out_features, in_features]
+        else:
+            weight_shape = [in_features, out_features]
+        dtype = self._helper.get_default_dtype()
+        self.weight = self.create_parameter(
+            shape=weight_shape, attr=weight_attr, dtype=dtype, is_bias=False)
+        self.bias = self.create_parameter(
+            shape=[out_features], attr=bias_attr, dtype=dtype, is_bias=True)
+        self.transpose_weight = transpose_weight
+        self.name = name
+
+    def forward(self, input):
+        return F.fused_linear(input, self.weight, self.bias,
+                              self.transpose_weight, self.name)