diff --git a/paddle/fluid/operators/batch_norm_op.cc b/paddle/fluid/operators/batch_norm_op.cc
index edad20435b41c9eb59c3df793c00ab3bfe96771b..b2cffc3f9063c1fd3b33baa9c740c2402fa00080 100644
--- a/paddle/fluid/operators/batch_norm_op.cc
+++ b/paddle/fluid/operators/batch_norm_op.cc
@@ -464,11 +464,9 @@ void BatchNormGradOp::InferShape(framework::InferShapeContext *ctx) const {
                  "BatchNormGrad");
 
   // check output
-  OP_INOUT_CHECK(ctx->HasOutput(framework::GradVarName("X")), "Output",
-                 framework::GradVarName("X"), "BatchNormGrad");
-
   const bool has_scale_grad = ctx->HasOutput(framework::GradVarName("Scale"));
   const bool has_bias_grad = ctx->HasOutput(framework::GradVarName("Bias"));
+  const bool has_x_grad = ctx->HasOutput(framework::GradVarName("X"));
 
   PADDLE_ENFORCE_EQ((has_scale_grad == has_bias_grad), true,
                     platform::errors::NotFound(
@@ -496,12 +494,14 @@ void BatchNormGradOp::InferShape(framework::InferShapeContext *ctx) const {
            ? x_dims[1]
            : x_dims[x_dims.size() - 1]);
 
-  ctx->SetOutputDim(framework::GradVarName("X"), x_dims);
   // has_scale_grad == has_bias_grad, judge has_scale_grad is enough
   if (has_scale_grad) {
     ctx->SetOutputDim(framework::GradVarName("Scale"), {C});
     ctx->SetOutputDim(framework::GradVarName("Bias"), {C});
   }
+  if (has_x_grad) {
+    ctx->SetOutputDim(framework::GradVarName("X"), x_dims);
+  }
 }
 
 framework::OpKernelType BatchNormGradOp::GetExpectedKernelType(
@@ -596,15 +596,20 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
     if (ctx.HasInput("Y")) {
       x = ctx.Input<Tensor>("Y");
       is_inplace = true;
-      PADDLE_ENFORCE_EQ(d_x, d_y,
-                        platform::errors::InvalidArgument(
-                            "X@GRAD and Y@GRAD not inplace in inplace mode"));
+      // if the input of batch norm is stop_gradient, d_x is null.
+      if (d_x) {
+        PADDLE_ENFORCE_EQ(d_x, d_y,
+                          platform::errors::InvalidArgument(
+                              "X@GRAD and Y@GRAD not inplace in inplace mode"));
+      }
     } else {
       x = ctx.Input<Tensor>("X");
       is_inplace = false;
-      PADDLE_ENFORCE_NE(d_x, d_y,
-                        platform::errors::InvalidArgument(
-                            "X@GRAD and Y@GRAD inplaced in non-inplace mode"));
+      if (d_x) {
+        PADDLE_ENFORCE_NE(
+            d_x, d_y, platform::errors::InvalidArgument(
+                          "X@GRAD and Y@GRAD inplaced in non-inplace mode"));
+      }
     }
 
     // Get the size for each dimension.
@@ -629,7 +634,9 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
     const int sample_size = x->numel() / N / C;
 
     // init output
-    d_x->mutable_data<T>(ctx.GetPlace());
+    if (d_x) {
+      d_x->mutable_data<T>(ctx.GetPlace());
+    }
 
     const T *mean_data = saved_mean->data<T>();
     const T *inv_var_data = saved_inv_variance->data<T>();
@@ -673,7 +680,7 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
       d_scale_arr.setZero();
     }
 
-    if ((N * sample_size) == 1 && !use_global_stats) {
+    if (d_x && (N * sample_size) == 1 && !use_global_stats) {
       framework::TensorCopy(*d_y, ctx.GetPlace(), d_x);
       return;
     }
@@ -718,8 +725,6 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
         }
         ConstEigenArrayMap<T> x_arr(x->data<T>(), sample_size, N * C);
         ConstEigenArrayMap<T> d_y_arr(d_y->data<T>(), sample_size, N * C);
-        EigenArrayMap<T> d_x_arr(d_x->mutable_data<T>(ctx.GetPlace()),
-                                 sample_size, N * C);
 
         for (int nc = 0; nc < N * C; ++nc) {
           int c = nc % C;
@@ -734,19 +739,24 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
           d_scale_arr = dy_mul_x_sub_mean_mul_invstd_sum_arr;
         }
 
-        if (!use_global_stats) {
-          for (int nc = 0; nc < N * C; ++nc) {
-            int c = nc % C;
-            d_x_arr.col(nc) =
-                scale_inv_var_nhw(c) *
-                (d_y_arr.col(nc) * N * sample_size - dy_sum_arr(c) -
-                 (x_arr.col(nc) - mean_arr[c]) *
-                     dy_mul_x_sub_mean_mul_invstd_sum_arr(c) * inv_var_arr(c));
-          }
-        } else {
-          for (int nc = 0; nc < N * C; ++nc) {
-            int c = nc % C;
-            d_x_arr.col(nc) = scale_inv_var_nhw(c) * d_y_arr.col(nc);
+        if (d_x) {
+          EigenArrayMap<T> d_x_arr(d_x->mutable_data<T>(ctx.GetPlace()),
+                                   sample_size, N * C);
+          if (!use_global_stats) {
+            for (int nc = 0; nc < N * C; ++nc) {
+              int c = nc % C;
+              d_x_arr.col(nc) =
+                  scale_inv_var_nhw(c) *
+                  (d_y_arr.col(nc) * N * sample_size - dy_sum_arr(c) -
+                   (x_arr.col(nc) - mean_arr[c]) *
+                       dy_mul_x_sub_mean_mul_invstd_sum_arr(c) *
+                       inv_var_arr(c));
+            }
+          } else {
+            for (int nc = 0; nc < N * C; ++nc) {
+              int c = nc % C;
+              d_x_arr.col(nc) = scale_inv_var_nhw(c) * d_y_arr.col(nc);
+            }
           }
         }
         break;
@@ -765,8 +775,6 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
         }
         ConstEigenArrayMap<T> x_arr(x->data<T>(), C, N * sample_size);
         ConstEigenArrayMap<T> d_y_arr(d_y->data<T>(), C, N * sample_size);
-        EigenArrayMap<T> d_x_arr(d_x->mutable_data<T>(ctx.GetPlace()), C,
-                                 N * sample_size);
 
         for (int nhw = 0; nhw < N * sample_size; ++nhw) {
           dy_sum_arr += d_y_arr.col(nhw);
@@ -779,17 +787,21 @@ class BatchNormGradKernel<platform::CPUDeviceContext, T>
           d_scale_arr = dy_mul_x_sub_mean_mul_invstd_sum_arr;
         }
 
-        if (!use_global_stats) {
-          for (int nhw = 0; nhw < N * sample_size; ++nhw) {
-            d_x_arr.col(nhw) =
-                scale_inv_var_nhw *
-                (d_y_arr.col(nhw) * N * sample_size - dy_sum_arr -
-                 (x_arr.col(nhw) - mean_arr) *
-                     dy_mul_x_sub_mean_mul_invstd_sum_arr * inv_var_arr);
-          }
-        } else {
-          for (int nhw = 0; nhw < N * sample_size; ++nhw) {
-            d_x_arr.col(nhw) = scale_inv_var_nhw * d_y_arr.col(nhw);
+        if (d_x) {
+          EigenArrayMap<T> d_x_arr(d_x->mutable_data<T>(ctx.GetPlace()), C,
+                                   N * sample_size);
+          if (!use_global_stats) {
+            for (int nhw = 0; nhw < N * sample_size; ++nhw) {
+              d_x_arr.col(nhw) =
+                  scale_inv_var_nhw *
+                  (d_y_arr.col(nhw) * N * sample_size - dy_sum_arr -
+                   (x_arr.col(nhw) - mean_arr) *
+                       dy_mul_x_sub_mean_mul_invstd_sum_arr * inv_var_arr);
+            }
+          } else {
+            for (int nhw = 0; nhw < N * sample_size; ++nhw) {
+              d_x_arr.col(nhw) = scale_inv_var_nhw * d_y_arr.col(nhw);
+            }
           }
         }
         break;
diff --git a/paddle/fluid/operators/batch_norm_op.cu b/paddle/fluid/operators/batch_norm_op.cu
index 42e1e2e7463c7753fbf205c88442db63733754ea..3d26c2c570858e11771fc27afabdcce5c0fb9443 100644
--- a/paddle/fluid/operators/batch_norm_op.cu
+++ b/paddle/fluid/operators/batch_norm_op.cu
@@ -840,15 +840,19 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
     if (ctx.HasInput("Y")) {
       x = ctx.Input<Tensor>("Y");
       is_inplace = true;
-      PADDLE_ENFORCE_EQ(d_x, d_y,
-                        platform::errors::InvalidArgument(
-                            "X@GRAD and Y@GRAD not inplace in inplace mode"));
+      if (d_x) {
+        PADDLE_ENFORCE_EQ(d_x, d_y,
+                          platform::errors::InvalidArgument(
+                              "X@GRAD and Y@GRAD not inplace in inplace mode"));
+      }
     } else {
       x = ctx.Input<Tensor>("X");
       is_inplace = false;
-      PADDLE_ENFORCE_NE(d_x, d_y,
-                        platform::errors::InvalidArgument(
-                            "X@GRAD and Y@GRAD inplaced in non-inplace mode"));
+      if (d_x) {
+        PADDLE_ENFORCE_NE(
+            d_x, d_y, platform::errors::InvalidArgument(
+                          "X@GRAD and Y@GRAD inplaced in non-inplace mode"));
+      }
     }
 
     const bool is_test = ctx.Attr<bool>("is_test");
@@ -867,7 +871,9 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
     ExtractNCWHD(x_dims, data_layout, &N, &C, &H, &W, &D);
 
     // init output
-    d_x->mutable_data<T>(ctx.GetPlace());
+    if (d_x) {
+      d_x->mutable_data<T>(ctx.GetPlace());
+    }
 
     if (d_scale && d_bias) {
       d_scale->mutable_data<BatchNormParamType<T>>(ctx.GetPlace());
@@ -908,7 +914,7 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
 
     Tensor transformed_x(x->type());
     Tensor transformed_d_y(d_y->type());
-    Tensor transformed_d_x(d_x->type());
+    Tensor transformed_d_x;
     if (data_layout == DataLayout::kNHWC &&
         compute_format == DataLayout::kNCHW) {
       VLOG(3) << "Transform input tensor from NHWC to NCHW.";
@@ -920,12 +926,16 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
                                                            &transformed_d_y);
       TransToChannelFirst<platform::CUDADeviceContext, T>(ctx, d_y,
                                                           &transformed_d_y);
-      ResizeToChannelFirst<platform::CUDADeviceContext, T>(ctx, d_x,
-                                                           &transformed_d_x);
+      if (d_x) {
+        ResizeToChannelFirst<platform::CUDADeviceContext, T>(ctx, d_x,
+                                                             &transformed_d_x);
+      }
     } else {
       transformed_x.ShareDataWith(*x);
       transformed_d_y.ShareDataWith(*d_y);
-      transformed_d_x.ShareDataWith(*d_x);
+      if (d_x) {
+        transformed_d_x.ShareDataWith(*d_x);
+      }
     }
 
     std::vector<int> dims;
@@ -954,7 +964,9 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
 
     if (!use_global_stats) {
       if ((N * H * W * D) == 1) {
-        framework::TensorCopy(*d_y, ctx.GetPlace(), d_x);
+        if (d_x) {
+          framework::TensorCopy(*d_y, ctx.GetPlace(), d_x);
+        }
         math::SetConstant<platform::CUDADeviceContext, BatchNormParamType<T>>
             functor;
         functor(dev_ctx, d_scale, static_cast<BatchNormParamType<T>>(0));
@@ -1042,7 +1054,7 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
       }
 
       // This branch calls CUDNN APIs
-      if (d_scale && d_bias) {
+      if (d_x && d_scale && d_bias) {
         bool called = false;
 #if CUDNN_VERSION_MIN(7, 4, 1)
         called = true;
@@ -1187,6 +1199,15 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
                 saved_mean_data, x->data<T>(), saved_var_data, C, N, H * W * D,
                 d_x->data<T>());
           }
+          if (d_scale && d_bias) {
+            KeBNBackwardScaleBias<
+                T, block,
+                framework::DataLayout::kNCHW><<<grid2, block, 0, stream>>>(
+                d_y->data<T>(), x->data<T>(), saved_mean_data, saved_var_data,
+                epsilon, N, C, H * W * D,
+                d_scale->data<BatchNormParamType<T>>(),
+                d_bias->data<BatchNormParamType<T>>());
+          }
         } else {
           if (d_x) {
             BNBackwardData<T, block, framework::DataLayout::kNHWC><<<
@@ -1195,6 +1216,15 @@ class BatchNormGradKernel<platform::CUDADeviceContext, T>
                 saved_mean_data, x->data<T>(), saved_var_data, C, N, H * W * D,
                 d_x->data<T>());
           }
+          if (d_scale && d_bias) {
+            KeBNBackwardScaleBias<
+                T, block,
+                framework::DataLayout::kNHWC><<<grid2, block, 0, stream>>>(
+                d_y->data<T>(), x->data<T>(), saved_mean_data, saved_var_data,
+                epsilon, N, C, H * W * D,
+                d_scale->data<BatchNormParamType<T>>(),
+                d_bias->data<BatchNormParamType<T>>());
+          }
         }
       }
 
diff --git a/python/paddle/fluid/tests/unittests/test_batch_norm_op.py b/python/paddle/fluid/tests/unittests/test_batch_norm_op.py
index 2eb334d09563129fb6555186d7e27497415e740f..9eaa69ce644285725987dac8a2d939e4ce798eca 100644
--- a/python/paddle/fluid/tests/unittests/test_batch_norm_op.py
+++ b/python/paddle/fluid/tests/unittests/test_batch_norm_op.py
@@ -515,6 +515,13 @@ class TestBatchNormOpTrainingCase2(TestBatchNormOpTraining):
         os.environ['FLAGS_cudnn_batchnorm_spatial_persistent'] = "1"
 
 
+class TestBatchNormOpTrainingCase3(TestBatchNormOpTraining):
+    def init_test_case(self):
+        self.use_global_stats = False
+        self.no_grad_set = set(['x@GRAD'])
+        self.fetch_list = ['y', 'mean', 'variance', 'scale@GRAD', 'bias@GRAD']
+
+
 class TestBatchNormOpTrainingMomentumVariable(TestBatchNormOpTraining):
     def init_test_case(self):
         self.use_momentum_variable = True