diff --git a/paddle/fluid/operators/kron_op.cc b/paddle/fluid/operators/kron_op.cc
index a98d56d6fcff091a9e35e14e130dba50dd0d2174..6f7aeb63b1ced096954d64c2882dabfca808acd6 100644
--- a/paddle/fluid/operators/kron_op.cc
+++ b/paddle/fluid/operators/kron_op.cc
@@ -99,17 +99,15 @@ class KronGradOp : public framework::OperatorWithKernel {
     OP_INOUT_CHECK(ctx->HasInput("Y"), "Input", "Y", "kron_grad");
     OP_INOUT_CHECK(ctx->HasInput(framework::GradVarName("Out")), "Input",
                    framework::GradVarName("Out"), "kron_grad");
-    OP_INOUT_CHECK(ctx->HasOutput(framework::GradVarName("X")), "Output",
-                   framework::GradVarName("X"), "kron_grad");
-    OP_INOUT_CHECK(ctx->HasOutput(framework::GradVarName("Y")), "Output",
-                   framework::GradVarName("Y"), "kron_grad");
 
     auto x_grad_name = framework::GradVarName("X");
     auto y_grad_name = framework::GradVarName("Y");
-    ctx->SetOutputDim(x_grad_name, ctx->GetInputDim("X"));
-    ctx->ShareLoD("X", /*->*/ x_grad_name);
-    ctx->SetOutputDim(y_grad_name, ctx->GetInputDim("Y"));
-    ctx->ShareLoD("Y", /*->*/ y_grad_name);
+    if (ctx->HasOutput(x_grad_name)) {
+      ctx->SetOutputDim(x_grad_name, ctx->GetInputDim("X"));
+    }
+    if (ctx->HasOutput(y_grad_name)) {
+      ctx->SetOutputDim(y_grad_name, ctx->GetInputDim("Y"));
+    }
   }
 
  protected:
diff --git a/paddle/fluid/operators/kron_op.h b/paddle/fluid/operators/kron_op.h
index ec7a8a7d9bb4dbd43843b5ea43fe781c92851d54..62762f3f049b6d60f0e4853bcdd46e39369c1158 100644
--- a/paddle/fluid/operators/kron_op.h
+++ b/paddle/fluid/operators/kron_op.h
@@ -147,11 +147,14 @@ struct KronGradElemFunctor {
       index_b += stride_b_[i] * pos_bi;
     }
 
-    size_t index_out_a = index_a * numel_b_ + index_b;
-    size_t index_out_b = index_b * numel_a_ + index_a;
-
-    dout_a_[index_out_a] = dout_[idx] * B_[index_b];
-    dout_b_[index_out_b] = dout_[idx] * A_[index_a];
+    if (dout_a_) {
+      size_t index_out_a = index_a * numel_b_ + index_b;
+      dout_a_[index_out_a] = dout_[idx] * B_[index_b];
+    }
+    if (dout_b_) {
+      size_t index_out_b = index_b * numel_a_ + index_a;
+      dout_b_[index_out_b] = dout_[idx] * A_[index_a];
+    }
   }
 
  private:
@@ -222,35 +225,50 @@ struct KronGradOpFunctor {
     // dout_x: dout * kron(ones(X), Y) re-aranged in shape (numel_x, numel_y)
     // dout_y: dout * kron(X, ones(Y)) re-aranged in shaoe (numel_y, numel_x)
     framework::Tensor dout_x;
-    dout_x.mutable_data<T>({numel_x, numel_y}, dev_ctx.GetPlace());
+    T* p_dout_x = nullptr;
+    if (dx) {
+      dout_x.mutable_data<T>({numel_x, numel_y}, dev_ctx.GetPlace());
+      p_dout_x = dout_x.data<T>();
+    }
     framework::Tensor dout_y;
-    dout_y.mutable_data<T>({numel_y, numel_x}, dev_ctx.GetPlace());
+    T* p_dout_y = nullptr;
+    if (dy) {
+      dout_y.mutable_data<T>({numel_y, numel_x}, dev_ctx.GetPlace());
+      p_dout_y = dout_y.data<T>();
+    }
 
     platform::ForRange<DeviceContext> for_range(dev_ctx, numel);
     KronGradElemFunctor<T> func(dout.data<T>(), x.data<T>(), y.data<T>(),
-                                dout_x.data<T>(), dout_y.data<T>(),
-                                p_stride_dout, p_stride_x, p_stride_y,
-                                p_shape_y, numel_x, numel_y, ndims);
+                                p_dout_x, p_dout_y, p_stride_dout, p_stride_x,
+                                p_stride_y, p_shape_y, numel_x, numel_y, ndims);
     for_range(func);
 
 // reduce_sum along aixs 1
 #if __NVCC__
     auto stream = dev_ctx.stream();  // it is a cuda device_context
-    TensorReduce<T, T, cub::Sum, IdentityFunctor<T>>(
-        dout_x, dx, {1}, static_cast<T>(0), cub::Sum(), IdentityFunctor<T>(),
-        stream);
-    TensorReduce<T, T, cub::Sum, IdentityFunctor<T>>(
-        dout_y, dy, {1}, static_cast<T>(0), cub::Sum(), IdentityFunctor<T>(),
-        stream);
+    if (dx) {
+      TensorReduce<T, T, cub::Sum, IdentityFunctor<T>>(
+          dout_x, dx, {1}, static_cast<T>(0), cub::Sum(), IdentityFunctor<T>(),
+          stream);
+    }
+    if (dy) {
+      TensorReduce<T, T, cub::Sum, IdentityFunctor<T>>(
+          dout_y, dy, {1}, static_cast<T>(0), cub::Sum(), IdentityFunctor<T>(),
+          stream);
+    }
 #else
-    auto eigen_dout_x = framework::EigenMatrix<T>::Reshape(dout_x, 1);
-    auto eigen_dout_y = framework::EigenMatrix<T>::Reshape(dout_y, 1);
-    auto eigen_vec_dx = framework::EigenVector<T>::Flatten(*dx);
-    auto eigen_vec_dy = framework::EigenVector<T>::Flatten(*dy);
     auto* place = dev_ctx.eigen_device();
     Eigen::array<int, 1> reduce_dim = {1};
-    eigen_vec_dx.device(*place) = eigen_dout_x.sum(reduce_dim);
-    eigen_vec_dy.device(*place) = eigen_dout_y.sum(reduce_dim);
+    if (dx) {
+      auto eigen_dout_x = framework::EigenMatrix<T>::Reshape(dout_x, 1);
+      auto eigen_vec_dx = framework::EigenVector<T>::Flatten(*dx);
+      eigen_vec_dx.device(*place) = eigen_dout_x.sum(reduce_dim);
+    }
+    if (dy) {
+      auto eigen_dout_y = framework::EigenMatrix<T>::Reshape(dout_y, 1);
+      auto eigen_vec_dy = framework::EigenVector<T>::Flatten(*dy);
+      eigen_vec_dy.device(*place) = eigen_dout_y.sum(reduce_dim);
+    }
 #endif
   }
 };
@@ -307,17 +325,33 @@ class KronGradKernel : public framework::OpKernel<T> {
 
     auto* dx = ctx.Output<framework::Tensor>(framework::GradVarName("X"));
     auto* dy = ctx.Output<framework::Tensor>(framework::GradVarName("Y"));
-    dx->mutable_data<T>(ctx.GetPlace());
-    dy->mutable_data<T>(ctx.GetPlace());
+    if (dx) {
+      dx->mutable_data<T>(ctx.GetPlace());
+    }
+    if (dy) {
+      dy->mutable_data<T>(ctx.GetPlace());
+    }
 
     int ndims = dout->dims().size();
     framework::Tensor xx = UnsqueezeTo(*x, ndims);
-    framework::Tensor dxx = UnsqueezeTo(*dx, ndims);
     framework::Tensor yy = UnsqueezeTo(*y, ndims);
-    framework::Tensor dyy = UnsqueezeTo(*dy, ndims);
+
+    framework::Tensor* pdxx = nullptr;
+    framework::Tensor* pdyy = nullptr;
+    framework::Tensor dxx;
+    framework::Tensor dyy;
+    if (dx) {
+      dxx = UnsqueezeTo(*dx, ndims);
+      pdxx = &dxx;
+    }
+
+    if (dy) {
+      dyy = UnsqueezeTo(*dy, ndims);
+      pdyy = &dyy;
+    }
 
     KronGradOpFunctor<DeviceContext, T> func;
-    func(dev_ctx, *dout, xx, yy, &dxx, &dyy);
+    func(dev_ctx, *dout, xx, yy, pdxx, pdyy);
   }
 };
 
diff --git a/python/paddle/complex/tensor/linalg.py b/python/paddle/complex/tensor/linalg.py
index 99c0ca5fbfab32c1581878f02db10d3338a507c8..fedfde5e5c2e00741b32fb4e2dc6ba58d5abb263 100644
--- a/python/paddle/complex/tensor/linalg.py
+++ b/python/paddle/complex/tensor/linalg.py
@@ -26,10 +26,10 @@ def matmul(x, y, transpose_x=False, transpose_y=False, alpha=1.0, name=None):
 
     Args:
         x (ComplexVariable|Variable): The first input, can be a ComplexVariable 
-            with data type complex32 or complex64, or a Variable with data type 
+            with data type complex64 or complex128, or a Variable with data type 
             float32 or float64.
         y (ComplexVariable|Variable): The second input, can be a ComplexVariable 
-            with data type complex32 or complex64, or a Variable with data type 
+            with data type complex64 or complex128, or a Variable with data type 
             float32 or float64.
         transpose_x (bool): Whether to transpose :math:`x` before multiplication.
         transpose_y (bool): Whether to transpose :math:`y` before multiplication.
diff --git a/python/paddle/complex/tensor/math.py b/python/paddle/complex/tensor/math.py
index 302782281c79b336b54657976c634fe1ecf5c09d..aa4d6a0fc5500d0210b37e74a47c0d8730c0666c 100644
--- a/python/paddle/complex/tensor/math.py
+++ b/python/paddle/complex/tensor/math.py
@@ -367,6 +367,7 @@ def kron(x, y, name=None):
     
             import numpy as np
             import paddle
+            from paddle import fluid
             import paddle.fluid.dygraph as dg
 
             a = np.array([[1.0+1.0j, 2.0+1.0j], [3.0+1.0j, 4.0+1.0j]])
diff --git a/python/paddle/fluid/tests/unittests/test_kron_op.py b/python/paddle/fluid/tests/unittests/test_kron_op.py
index 2474c0738c1424869e64791cc82699f288f398b0..556d68955328f072b2fedc66d668c9a9875f57f7 100644
--- a/python/paddle/fluid/tests/unittests/test_kron_op.py
+++ b/python/paddle/fluid/tests/unittests/test_kron_op.py
@@ -42,6 +42,12 @@ class TestKronOp(OpTest):
     def test_check_grad(self):
         self.check_grad(['X', 'Y'], 'Out')
 
+    def test_check_grad_ignore_x(self):
+        self.check_grad(['Y'], 'Out', no_grad_set=set('X'))
+
+    def test_check_grad_ignore_y(self):
+        self.check_grad(['X'], 'Out', no_grad_set=set('Y'))
+
 
 class TestKronOp2(TestKronOp):
     def setUp(self):
diff --git a/python/paddle/fluid/tests/unittests/white_list/no_grad_set_white_list.py b/python/paddle/fluid/tests/unittests/white_list/no_grad_set_white_list.py
index eb1471e377a0b7e1bd2eb59a37ab3eba5c6b59e7..330cf5a72b1a56f674c82d4fb9e502785e2cf5c0 100644
--- a/python/paddle/fluid/tests/unittests/white_list/no_grad_set_white_list.py
+++ b/python/paddle/fluid/tests/unittests/white_list/no_grad_set_white_list.py
@@ -13,7 +13,7 @@
 # limitations under the License.
 
 # check no_grad_set is None
-NOT_CHECK_OP_LIST = ['deformable_conv', 'row_conv']
+NOT_CHECK_OP_LIST = ['deformable_conv', 'row_conv', 'kron']
 
 # TODO(Shixiaowei02): Check if the items do not need fix.
 # no_grad_set has value in NEED_TO_FIX_OP_LIST