diff --git a/paddle/fluid/operators/reduce_ops/logsumexp_op.cc b/paddle/fluid/operators/reduce_ops/logsumexp_op.cc
index 9f0ef19bd6299cae2f1538377b58a3e97eafe7c0..0602c73db6bbc92727c5a5d7673a4d0c20265458 100644
--- a/paddle/fluid/operators/reduce_ops/logsumexp_op.cc
+++ b/paddle/fluid/operators/reduce_ops/logsumexp_op.cc
@@ -12,10 +12,13 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "paddle/fluid/operators/reduce_ops/logsumexp_op.h"
 #include <algorithm>
 #include <string>
 #include <vector>
+#include "paddle/fluid/framework/infershape_utils.h"
+#include "paddle/fluid/operators/reduce_ops/reduce_op_function.h"
+#include "paddle/phi/core/infermeta_utils.h"
+#include "paddle/phi/infermeta/unary.h"
 
 namespace paddle {
 namespace operators {
@@ -23,80 +26,6 @@ namespace operators {
 class LogsumexpOp : public framework::OperatorWithKernel {
  public:
   using framework::OperatorWithKernel::OperatorWithKernel;
-
-  void InferShape(framework::InferShapeContext* ctx) const override {
-    OP_INOUT_CHECK(ctx->HasInput("X"), "Input", "X", "logsumexp");
-    OP_INOUT_CHECK(ctx->HasOutput("Out"), "Output", "Out", "logsumexp");
-    auto x_dims = ctx->GetInputDim("X");
-    auto x_rank = x_dims.size();
-    PADDLE_ENFORCE_LE(x_rank, 4,
-                      platform::errors::InvalidArgument(
-                          "The input tensor X's dimensions of logsumexp "
-                          "should be less or equal than 4. But received X's "
-                          "dimensions = %d, X's shape = [%s].",
-                          x_rank, x_dims));
-    auto axis = ctx->Attrs().Get<std::vector<int>>("axis");
-    PADDLE_ENFORCE_GT(
-        axis.size(), 0,
-        platform::errors::InvalidArgument(
-            "The size of axis of logsumexp "
-            "should be greater than 0. But received the size of axis "
-            "of logsumexp is %d.",
-            axis.size()));
-
-    for (size_t i = 0; i < axis.size(); i++) {
-      PADDLE_ENFORCE_LT(axis[i], x_rank,
-                        platform::errors::InvalidArgument(
-                            "axis[%d] should be in the "
-                            "range [-D, D), where D is the dimensions of X and "
-                            "D is %d. But received axis[%d] = %d.",
-                            i, x_rank, i, axis[i]));
-      PADDLE_ENFORCE_GE(axis[i], -x_rank,
-                        platform::errors::InvalidArgument(
-                            "axis[%d] should be in the "
-                            "range [-D, D), where D is the dimensions of X and "
-                            "D is %d. But received axis[%d] = %d.",
-                            i, x_rank, i, axis[i]));
-      if (axis[i] < 0) {
-        axis[i] += x_rank;
-      }
-    }
-
-    bool keepdim = ctx->Attrs().Get<bool>("keepdim");
-    bool reduce_all = ctx->Attrs().Get<bool>("reduce_all");
-    auto dims_vector = vectorize(x_dims);
-    if (reduce_all) {
-      if (keepdim)
-        ctx->SetOutputDim("Out",
-                          phi::make_ddim(std::vector<int64_t>(x_rank, 1)));
-      else
-        ctx->SetOutputDim("Out", {1});
-    } else {
-      auto dims_vector = vectorize(x_dims);
-      if (keepdim) {
-        for (size_t i = 0; i < axis.size(); ++i) {
-          dims_vector[axis[i]] = 1;
-        }
-      } else {
-        const int kDelFlag = -1;
-        for (size_t i = 0; i < axis.size(); ++i) {
-          dims_vector[axis[i]] = kDelFlag;
-        }
-        dims_vector.erase(
-            std::remove(dims_vector.begin(), dims_vector.end(), kDelFlag),
-            dims_vector.end());
-      }
-      if (!keepdim && dims_vector.size() == 0) {
-        dims_vector.push_back(1);
-      }
-      auto out_dims = phi::make_ddim(dims_vector);
-      ctx->SetOutputDim("Out", out_dims);
-      if (axis.size() > 0 && axis[0] != 0) {
-        // Only pass LoD when not reducing on the first dim.
-        ctx->ShareLoD("X", /*->*/ "Out");
-      }
-    }
-  }
 };
 
 class LogsumexpOpMaker : public framework::OpProtoAndCheckerMaker {
@@ -164,16 +93,10 @@ class LogsumexpGradOpMaker : public framework::SingleGradOpMaker<T> {
 }  // namespace paddle
 
 namespace ops = paddle::operators;
-
+DECLARE_INFER_SHAPE_FUNCTOR(logsumexp, LogsumexpInferShapeFunctor,
+                            PD_INFER_META(phi::LogsumexpInferMeta));
 REGISTER_OPERATOR(logsumexp, ops::LogsumexpOp, ops::LogsumexpOpMaker,
                   ops::LogsumexpGradOpMaker<paddle::framework::OpDesc>,
-                  ops::LogsumexpGradOpMaker<paddle::imperative::OpBase>);
+                  ops::LogsumexpGradOpMaker<paddle::imperative::OpBase>,
+                  LogsumexpInferShapeFunctor);
 REGISTER_OPERATOR(logsumexp_grad, ops::LogsumexpGrapOp);
-
-REGISTER_OP_CPU_KERNEL(
-    logsumexp, ops::LogsumexpKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::LogsumexpKernel<paddle::platform::CPUDeviceContext, double>);
-REGISTER_OP_CPU_KERNEL(
-    logsumexp_grad,
-    ops::LogsumexpGradKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::LogsumexpGradKernel<paddle::platform::CPUDeviceContext, double>);
diff --git a/paddle/fluid/operators/reduce_ops/logsumexp_op.h b/paddle/fluid/operators/reduce_ops/logsumexp_op.h
deleted file mode 100644
index 4490f08b2129ad0a1dfcd42602ce1ad6f694d1f7..0000000000000000000000000000000000000000
--- a/paddle/fluid/operators/reduce_ops/logsumexp_op.h
+++ /dev/null
@@ -1,170 +0,0 @@
-// Copyright (c) 2020 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.
-
-#pragma once
-
-#include <algorithm>
-#include <vector>
-#include "paddle/fluid/operators/reduce_ops/reduce_op_function.h"
-
-namespace paddle {
-namespace operators {
-
-#define HANDLE_DIM(NDIM, RDIM)                                            \
-  if (ndim == NDIM && rdim == RDIM) {                                     \
-    paddle::operators::ReduceFunctor<DeviceContext, OutT, NDIM, RDIM,     \
-                                     LogsumexpFunctor>(                   \
-        context.template device_context<DeviceContext>(), *input, output, \
-        axis, keepdim);                                                   \
-  }
-
-struct LogsumexpFunctor {
-  template <typename DeviceContext, typename X, typename Y, typename Dim>
-  void operator()(const DeviceContext& place, X* x, Y* y, const Dim& dim) {
-    auto x_dim = x->dimensions();
-    auto t_dim = x_dim;
-    for (int i = 0; i < static_cast<int>(dim.size()); i++) {
-      t_dim[dim[i]] = 1;
-    }
-
-    auto r_dim = x_dim;
-    for (int i = 0; i < static_cast<int>(r_dim.size()); i++) {
-      r_dim[i] = 1;
-    }
-    for (int i = 0; i < static_cast<int>(dim.size()); i++) {
-      r_dim[dim[i]] = x_dim[dim[i]];
-    }
-
-    auto y_dim = y->dimensions();
-    auto x_max = x->maximum(dim);
-    y->device(place) =
-        (x_max +
-         (*x - x_max.reshape(t_dim).broadcast(r_dim)).exp().sum(dim).log())
-            .reshape(y_dim);
-  }
-};
-
-struct LogsumexpGradFunctor {
-  template <typename DeviceContext, typename X, typename Y, typename DX,
-            typename DY, typename Dim>
-  void operator()(const DeviceContext& place, X* x, Y* y, DX* dx, DY* dy,
-                  const Dim& dim, int size) {
-    dx->device(place) = dy->broadcast(dim) * (*x - y->broadcast(dim)).exp();
-  }
-};
-
-template <typename DeviceContext, typename OutT>
-class LogsumexpKernel : public framework::OpKernel<OutT> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    auto* input = context.Input<Tensor>("X");
-    auto* output = context.Output<Tensor>("Out");
-    output->mutable_data<OutT>(context.GetPlace());
-
-    auto axis = context.Attr<std::vector<int>>("axis");
-    auto keepdim = context.Attr<bool>("keepdim");
-    auto reduce_all = context.Attr<bool>("reduce_all");
-
-    const auto& input_dim_size = input->dims().size();
-    // The dims has full dim, set the reduce_all is True
-    reduce_all |= (static_cast<const int>(axis.size()) == input_dim_size);
-
-    if (reduce_all) {
-      // Flatten and reduce 1-D tensor
-      auto x = EigenVector<OutT>::Flatten(*input);
-      auto out = EigenScalar<OutT>::From(*output);
-      auto& place =
-          *context.template device_context<DeviceContext>().eigen_device();
-      auto reduce_dim = Eigen::array<int, 1>({{0}});
-      LogsumexpFunctor()(place, &x, &out, reduce_dim);
-    } else {
-      int ndim = input_dim_size;
-      int rdim = axis.size();
-      // comments for accelerating compiling temporarily.
-      // HANDLE_DIM(6, 5);
-      // HANDLE_DIM(6, 4);
-      // HANDLE_DIM(6, 3);
-      // HANDLE_DIM(6, 2);
-      // HANDLE_DIM(6, 1);
-      // HANDLE_DIM(5, 4);
-      // HANDLE_DIM(5, 3);
-      // HANDLE_DIM(5, 2);
-      // HANDLE_DIM(5, 1);
-      HANDLE_DIM(4, 3);
-      HANDLE_DIM(4, 2);
-      HANDLE_DIM(4, 1);
-      HANDLE_DIM(3, 2);
-      HANDLE_DIM(3, 1);
-      HANDLE_DIM(2, 1);
-    }
-  }
-};
-
-template <typename DeviceContext, typename T>
-class LogsumexpGradKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    auto* input = context.Input<Tensor>("X");
-    auto* output = context.Input<Tensor>("Out");
-    auto* output_grad = context.Input<Tensor>(framework::GradVarName("Out"));
-    auto* input_grad = context.Output<Tensor>(framework::GradVarName("X"));
-    input_grad->mutable_data<T>(context.GetPlace());
-
-    auto axis = context.Attr<std::vector<int>>("axis");
-    auto reduce_all = context.Attr<bool>("reduce_all");
-    const auto input_dim_size = context.Input<Tensor>("X")->dims().size();
-    reduce_all |= (static_cast<const int>(axis.size()) == input_dim_size);
-
-    if (reduce_all) {
-      auto x = EigenVector<T>::Flatten(*input);
-      auto y = EigenVector<T>::Flatten(*output);
-      auto dy = EigenVector<T>::Flatten(*output_grad);
-      auto dx = EigenVector<T>::Flatten(*input_grad);
-      auto& place =
-          *context.template device_context<DeviceContext>().eigen_device();
-      auto broadcast_dim =
-          Eigen::array<int, 1>({{static_cast<int>(input->numel())}});
-      LogsumexpGradFunctor()(place, &x, &y, &dx, &dy, broadcast_dim,
-                             broadcast_dim[0]);
-    } else {
-      int rank = input->dims().size();
-      LogsumexpGradFunctor functor;
-      switch (rank) {
-        case 1:
-          ReduceGradFunctor<DeviceContext, T, 1, LogsumexpGradFunctor>(
-              context.template device_context<DeviceContext>(), *input, *output,
-              *output_grad, input_grad, functor, axis);
-          break;
-        case 2:
-          ReduceGradFunctor<DeviceContext, T, 2, LogsumexpGradFunctor>(
-              context.template device_context<DeviceContext>(), *input, *output,
-              *output_grad, input_grad, functor, axis);
-          break;
-        case 3:
-          ReduceGradFunctor<DeviceContext, T, 3, LogsumexpGradFunctor>(
-              context.template device_context<DeviceContext>(), *input, *output,
-              *output_grad, input_grad, functor, axis);
-          break;
-        case 4:
-          ReduceGradFunctor<DeviceContext, T, 4, LogsumexpGradFunctor>(
-              context.template device_context<DeviceContext>(), *input, *output,
-              *output_grad, input_grad, functor, axis);
-          break;
-      }
-    }
-  }
-};
-
-}  // namespace operators
-}  // namespace paddle
diff --git a/paddle/fluid/operators/reduce_ops/logsumexp_op_xpu.cc b/paddle/fluid/operators/reduce_ops/logsumexp_op_xpu.cc
index dcb849de0991bc93514a33d8ba93a6fe84d87093..6fb60fa1791571657d932edbec0b697544d3045e 100644
--- a/paddle/fluid/operators/reduce_ops/logsumexp_op_xpu.cc
+++ b/paddle/fluid/operators/reduce_ops/logsumexp_op_xpu.cc
@@ -14,7 +14,7 @@
 
 #ifdef PADDLE_WITH_XPU
 
-#include "paddle/fluid/operators/reduce_ops/logsumexp_op.h"
+#include "paddle/fluid/operators/reduce_ops/reduce_op_function.h"
 #include "paddle/fluid/platform/device/xpu/xpu_header.h"
 #include "paddle/fluid/platform/device_context.h"
 
diff --git a/paddle/phi/infermeta/unary.cc b/paddle/phi/infermeta/unary.cc
index 9761f902c70adce29a591d109f5ee4fed9ee8bab..c5cc845625479dd76cf13bb82f96dae221af6ecc 100644
--- a/paddle/phi/infermeta/unary.cc
+++ b/paddle/phi/infermeta/unary.cc
@@ -804,6 +804,91 @@ void KthvalueInferMeta(const MetaTensor& x,
   indices->set_dtype(x.dtype());
 }
 
+void LogsumexpInferMeta(const MetaTensor& input,
+                        const std::vector<int64_t>& axis,
+                        bool keepdim,
+                        bool reduce_all,
+                        MetaTensor* out) {
+  auto x_dims = input.dims();
+  auto x_rank = x_dims.size();
+  std::vector<int64_t> formated_axis = axis;
+  PADDLE_ENFORCE_LE(x_rank,
+                    4,
+                    errors::InvalidArgument(
+                        "The input tensor X's dimensions of logsumexp "
+                        "should be less or equal than 4. But received X's "
+                        "dimensions = %d, X's shape = [%s].",
+                        x_rank,
+                        x_dims));
+  PADDLE_ENFORCE_GT(
+      axis.size(),
+      0,
+      errors::InvalidArgument(
+          "The size of axis of logsumexp "
+          "should be greater than 0. But received the size of axis "
+          "of logsumexp is %d.",
+          axis.size()));
+
+  for (size_t i = 0; i < axis.size(); i++) {
+    PADDLE_ENFORCE_LT(axis[i],
+                      x_rank,
+                      errors::InvalidArgument(
+                          "axis[%d] should be in the "
+                          "range [-D, D), where D is the dimensions of X and "
+                          "D is %d. But received axis[%d] = %d.",
+                          i,
+                          x_rank,
+                          i,
+                          axis[i]));
+    PADDLE_ENFORCE_GE(axis[i],
+                      -x_rank,
+                      errors::InvalidArgument(
+                          "axis[%d] should be in the "
+                          "range [-D, D), where D is the dimensions of X and "
+                          "D is %d. But received axis[%d] = %d.",
+                          i,
+                          x_rank,
+                          i,
+                          axis[i]));
+    if (axis[i] < 0) {
+      formated_axis[i] += x_rank;
+    }
+  }
+
+  auto dims_vector = vectorize(x_dims);
+  if (reduce_all) {
+    if (keepdim)
+      out->set_dims(phi::make_ddim(std::vector<int64_t>(x_rank, 1)));
+    else
+      out->set_dims({1});
+  } else {
+    auto dims_vector = vectorize(x_dims);
+    if (keepdim) {
+      for (size_t i = 0; i < formated_axis.size(); ++i) {
+        dims_vector[formated_axis[i]] = 1;
+      }
+    } else {
+      const int kDelFlag = -1;
+      for (size_t i = 0; i < formated_axis.size(); ++i) {
+        dims_vector[formated_axis[i]] = kDelFlag;
+      }
+      dims_vector.erase(
+          std::remove(dims_vector.begin(), dims_vector.end(), kDelFlag),
+          dims_vector.end());
+    }
+    if (!keepdim && dims_vector.size() == 0) {
+      dims_vector.push_back(1);
+    }
+    auto out_dims = phi::make_ddim(dims_vector);
+    out->set_dims(out_dims);
+    if (formated_axis.size() > 0 && formated_axis[0] != 0) {
+      // Only pass LoD when not reducing on the first dim.
+      out->share_lod(input);
+    }
+  }
+  out->set_dtype(input.dtype());
+}
+
 void MatrixPowerInferMeta(const MetaTensor& x, int n, MetaTensor* out) {
   auto dims = x.dims();
   auto n_dim = dims.size();
diff --git a/paddle/phi/infermeta/unary.h b/paddle/phi/infermeta/unary.h
index 8a9876b11625c5aeaafac744496ff4240ec8cde0..3b6a34cff610dc4db85a906456842b467a851783 100644
--- a/paddle/phi/infermeta/unary.h
+++ b/paddle/phi/infermeta/unary.h
@@ -136,6 +136,12 @@ void KthvalueInferMeta(const MetaTensor& x,
                        MetaTensor* indices,
                        MetaConfig = MetaConfig());
 
+void LogsumexpInferMeta(const MetaTensor& input,
+                        const std::vector<int64_t>& axis,
+                        bool keepdim,
+                        bool reduce_all,
+                        MetaTensor* out);
+
 void MatrixPowerInferMeta(const MetaTensor& x, int n, MetaTensor* out);
 
 void MaxOutInferMeta(const MetaTensor& x,
diff --git a/paddle/fluid/operators/reduce_ops/logsumexp_op.part.cu b/paddle/phi/kernels/cpu/logsumexp_grad_kernel.cc
similarity index 58%
rename from paddle/fluid/operators/reduce_ops/logsumexp_op.part.cu
rename to paddle/phi/kernels/cpu/logsumexp_grad_kernel.cc
index 81124e4f070a54444f4305dc903280548ac10b60..e0ef67084b445ea354e002ee1df836065afcc78f 100644
--- a/paddle/fluid/operators/reduce_ops/logsumexp_op.part.cu
+++ b/paddle/phi/kernels/cpu/logsumexp_grad_kernel.cc
@@ -1,4 +1,4 @@
-// Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+// 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.
@@ -12,12 +12,11 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-// .part used to speed up nvcc compile
-#include "paddle/fluid/operators/reduce_ops/logsumexp_op.h"
+#include "paddle/phi/kernels/logsumexp_grad_kernel.h"
 
-namespace ops = paddle::operators;
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/impl/logsumexp_grad_kernel_impl.h"
 
-REGISTER_OP_CUDA_KERNEL(
-    logsumexp_grad,
-    ops::LogsumexpGradKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::LogsumexpGradKernel<paddle::platform::CUDADeviceContext, double>);
+PD_REGISTER_KERNEL(
+    logsumexp_grad, CPU, ALL_LAYOUT, phi::LogsumexpGradKernel, float, double) {}
diff --git a/paddle/fluid/operators/reduce_ops/logsumexp_op.cu b/paddle/phi/kernels/cpu/logsumexp_kernel.cc
similarity index 61%
rename from paddle/fluid/operators/reduce_ops/logsumexp_op.cu
rename to paddle/phi/kernels/cpu/logsumexp_kernel.cc
index 86a31595ebaabcbc07fab64779c33566d5b020eb..06e0b30a9ca6567d04f7946a1732fd1483289e03 100644
--- a/paddle/fluid/operators/reduce_ops/logsumexp_op.cu
+++ b/paddle/phi/kernels/cpu/logsumexp_kernel.cc
@@ -1,4 +1,4 @@
-// Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+// 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.
@@ -12,10 +12,12 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "paddle/fluid/operators/reduce_ops/logsumexp_op.h"
+#include "paddle/phi/kernels/logsumexp_kernel.h"
 
-namespace ops = paddle::operators;
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
 
-REGISTER_OP_CUDA_KERNEL(
-    logsumexp, ops::LogsumexpKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::LogsumexpKernel<paddle::platform::CUDADeviceContext, double>);
+#include "paddle/phi/kernels/impl/logsumexp_kernel_impl.h"
+
+PD_REGISTER_KERNEL(
+    logsumexp, CPU, ALL_LAYOUT, phi::LogsumexpKernel, float, double) {}
diff --git a/paddle/phi/kernels/gpu/logsumexp_grad_kernel.cu b/paddle/phi/kernels/gpu/logsumexp_grad_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..490b3e94045612cea551db515d273c7a0ef2c577
--- /dev/null
+++ b/paddle/phi/kernels/gpu/logsumexp_grad_kernel.cu
@@ -0,0 +1,22 @@
+// 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.
+
+#include "paddle/phi/kernels/logsumexp_grad_kernel.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/impl/logsumexp_grad_kernel_impl.h"
+
+PD_REGISTER_KERNEL(
+    logsumexp_grad, GPU, ALL_LAYOUT, phi::LogsumexpGradKernel, float, double) {}
diff --git a/paddle/phi/kernels/gpu/logsumexp_kernel.cu b/paddle/phi/kernels/gpu/logsumexp_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..0f07a39ab113ae42ff0bd634c92f571979f51127
--- /dev/null
+++ b/paddle/phi/kernels/gpu/logsumexp_kernel.cu
@@ -0,0 +1,23 @@
+// 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.
+
+#include "paddle/phi/kernels/logsumexp_kernel.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+#include "paddle/phi/kernels/impl/logsumexp_kernel_impl.h"
+
+PD_REGISTER_KERNEL(
+    logsumexp, GPU, ALL_LAYOUT, phi::LogsumexpKernel, float, double) {}
diff --git a/paddle/phi/kernels/impl/logsumexp_grad_kernel_impl.h b/paddle/phi/kernels/impl/logsumexp_grad_kernel_impl.h
new file mode 100644
index 0000000000000000000000000000000000000000..c2583ce8d32df7aedbc9022f1eac0b85e9d7d082
--- /dev/null
+++ b/paddle/phi/kernels/impl/logsumexp_grad_kernel_impl.h
@@ -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.
+
+#pragma once
+#include <type_traits>
+#include <vector>
+
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+#include "paddle/phi/kernels/funcs/eigen/eigen_function.h"
+#include "paddle/phi/kernels/funcs/reduce_grad_functions.h"
+#include "paddle/phi/kernels/logsumexp_grad_kernel.h"
+
+namespace phi {
+
+struct LogsumexpGradFunctor {
+  template <typename Context,
+            typename X,
+            typename Y,
+            typename DX,
+            typename DY,
+            typename Dim>
+  void operator()(const Context& place,
+                  X* x,
+                  Y* y,
+                  DX* dx,
+                  DY* dy,
+                  const Dim& dim,
+                  int size) {
+    dx->device(place) = dy->broadcast(dim) * (*x - y->broadcast(dim)).exp();
+  }
+};
+
+template <typename T, typename Context>
+void LogsumexpGradKernel(const Context& dev_ctx,
+                         const DenseTensor& in,
+                         const DenseTensor& out,
+                         const DenseTensor& out_grad,
+                         const std::vector<int>& axis,
+                         bool keepdim,
+                         bool reduce_all,
+                         DenseTensor* in_grad) {
+  dev_ctx.template Alloc<T>(in_grad);
+
+  const auto input_dim_size = in.dims().size();
+  reduce_all |= (static_cast<const int>(axis.size()) == input_dim_size);
+
+  if (reduce_all) {
+    auto x = phi::EigenVector<T>::Flatten(in);
+    auto y = phi::EigenVector<T>::Flatten(out);
+    auto dy = phi::EigenVector<T>::Flatten(out_grad);
+    auto dx = phi::EigenVector<T>::Flatten(*in_grad);
+    auto& place = *dev_ctx.eigen_device();
+    auto broadcast_dim = Eigen::array<int, 1>({{static_cast<int>(in.numel())}});
+    LogsumexpGradFunctor()(
+        place, &x, &y, &dx, &dy, broadcast_dim, broadcast_dim[0]);
+  } else {
+    int rank = in.dims().size();
+    LogsumexpGradFunctor functor;
+    switch (rank) {
+      case 1:
+        phi::funcs::ReduceGradFunctor<Context, T, 1, LogsumexpGradFunctor>(
+            dev_ctx, in, out, out_grad, in_grad, functor, axis);
+        break;
+      case 2:
+        phi::funcs::ReduceGradFunctor<Context, T, 2, LogsumexpGradFunctor>(
+            dev_ctx, in, out, out_grad, in_grad, functor, axis);
+        break;
+      case 3:
+        phi::funcs::ReduceGradFunctor<Context, T, 3, LogsumexpGradFunctor>(
+            dev_ctx, in, out, out_grad, in_grad, functor, axis);
+        break;
+      case 4:
+        phi::funcs::ReduceGradFunctor<Context, T, 4, LogsumexpGradFunctor>(
+            dev_ctx, in, out, out_grad, in_grad, functor, axis);
+        break;
+    }
+  }
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/impl/logsumexp_kernel_impl.h b/paddle/phi/kernels/impl/logsumexp_kernel_impl.h
new file mode 100644
index 0000000000000000000000000000000000000000..7a9573ff522b0a2f3c9cc62e39054c434b55282d
--- /dev/null
+++ b/paddle/phi/kernels/impl/logsumexp_kernel_impl.h
@@ -0,0 +1,100 @@
+// 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.
+
+#pragma once
+#include <type_traits>
+#include <vector>
+
+#include "paddle/phi/kernels/cpu/reduce.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+#include "paddle/phi/kernels/funcs/eigen/eigen_function.h"
+#include "paddle/phi/kernels/logsumexp_kernel.h"
+
+namespace phi {
+
+#define HANDLE_DIM(NDIM, RDIM)                               \
+  if (ndim == NDIM && rdim == RDIM) {                        \
+    ReduceFunctor<Context, T, NDIM, RDIM, LogsumexpFunctor>( \
+        dev_ctx, x, out, axis, keepdim);                     \
+  }
+
+struct LogsumexpFunctor {
+  template <typename Context, typename X, typename Y, typename Dim>
+  void operator()(const Context& place, X* x, Y* y, const Dim& dim) {
+    auto x_dim = x->dimensions();
+    auto t_dim = x_dim;
+    for (int i = 0; i < static_cast<int>(dim.size()); i++) {
+      t_dim[dim[i]] = 1;
+    }
+
+    auto r_dim = x_dim;
+    for (int i = 0; i < static_cast<int>(r_dim.size()); i++) {
+      r_dim[i] = 1;
+    }
+    for (int i = 0; i < static_cast<int>(dim.size()); i++) {
+      r_dim[dim[i]] = x_dim[dim[i]];
+    }
+
+    auto y_dim = y->dimensions();
+    auto x_max = x->maximum(dim);
+    y->device(place) =
+        (x_max +
+         (*x - x_max.reshape(t_dim).broadcast(r_dim)).exp().sum(dim).log())
+            .reshape(y_dim);
+  }
+};
+
+template <typename T, typename Context>
+void LogsumexpKernel(const Context& dev_ctx,
+                     const DenseTensor& x,
+                     const std::vector<int64_t>& axis,
+                     bool keepdim,
+                     bool reduce_all,
+                     DenseTensor* out) {
+  dev_ctx.template Alloc<T>(out);
+
+  const auto& input_dim_size = x.dims().size();
+  // The dims has full dim, set the reduce_all is True
+  reduce_all |= (static_cast<const int>(axis.size()) == input_dim_size);
+
+  if (reduce_all) {
+    // Flatten and reduce 1-D tensor
+    auto input = phi::EigenVector<T>::Flatten(x);
+    auto output = phi::EigenScalar<T>::From(*out);
+    auto& place = *dev_ctx.eigen_device();
+    auto reduce_dim = Eigen::array<int, 1>({{0}});
+    LogsumexpFunctor()(place, &input, &output, reduce_dim);
+  } else {
+    int ndim = input_dim_size;
+    int rdim = axis.size();
+    // comments for accelerating compiling temporarily.
+    // HANDLE_DIM(6, 5);
+    // HANDLE_DIM(6, 4);
+    // HANDLE_DIM(6, 3);
+    // HANDLE_DIM(6, 2);
+    // HANDLE_DIM(6, 1);
+    // HANDLE_DIM(5, 4);
+    // HANDLE_DIM(5, 3);
+    // HANDLE_DIM(5, 2);
+    // HANDLE_DIM(5, 1);
+    HANDLE_DIM(4, 3);
+    HANDLE_DIM(4, 2);
+    HANDLE_DIM(4, 1);
+    HANDLE_DIM(3, 2);
+    HANDLE_DIM(3, 1);
+    HANDLE_DIM(2, 1);
+  }
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/logsumexp_grad_kernel.h b/paddle/phi/kernels/logsumexp_grad_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..d68c447aa65cb2970e4f8897042f81acffce454f
--- /dev/null
+++ b/paddle/phi/kernels/logsumexp_grad_kernel.h
@@ -0,0 +1,31 @@
+// 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void LogsumexpGradKernel(const Context& ctx,
+                         const DenseTensor& in,
+                         const DenseTensor& out,
+                         const DenseTensor& out_grad,
+                         const std::vector<int>& axis,
+                         bool keepdim,
+                         bool reduce_all,
+                         DenseTensor* in_grad);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/logsumexp_kernel.h b/paddle/phi/kernels/logsumexp_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..ba1b18230fa52845bede77331cadd8d61bbd5244
--- /dev/null
+++ b/paddle/phi/kernels/logsumexp_kernel.h
@@ -0,0 +1,29 @@
+// 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void LogsumexpKernel(const Context& ctx,
+                     const DenseTensor& x,
+                     const std::vector<int64_t>& axis,
+                     bool keepdim,
+                     bool reduce_all,
+                     DenseTensor* out);
+
+}  // namespace phi
diff --git a/paddle/phi/ops/compat/logsumexp_sig.cc b/paddle/phi/ops/compat/logsumexp_sig.cc
new file mode 100644
index 0000000000000000000000000000000000000000..ca7345dbe704999183a784489f13bea05e30fdc0
--- /dev/null
+++ b/paddle/phi/ops/compat/logsumexp_sig.cc
@@ -0,0 +1,29 @@
+// 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.
+
+#include "paddle/phi/core/compat/op_utils.h"
+
+namespace phi {
+
+KernelSignature LogsumexpGradOpArgumentMapping(
+    const ArgumentMappingContext& ctx) {
+  return KernelSignature("logsumexp_grad",
+                         {"X", "Out", GradVarName("Out")},
+                         {"axis", "keepdim", "reduce_all"},
+                         {GradVarName("X")});
+}
+
+}  // namespace phi
+
+PD_REGISTER_ARG_MAPPING_FN(logsumexp_grad, phi::LogsumexpGradOpArgumentMapping);