diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index 81a55a42b483d34291ccb32e7284820cfb3b9974..6f86b62b48d1d00d5c565241d5e78c57f1adf5db 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -301,4 +301,36 @@ TEST(Backward, op_part_of_input_are_not_need) {
             "b" + f::OperatorBase::GRAD_VAR_SUFFIX());
   ASSERT_EQ(grad_mul.Input("Out" + f::OperatorBase::GRAD_VAR_SUFFIX()),
             "out" + f::OperatorBase::GRAD_VAR_SUFFIX());
+  ASSERT_EQ(grad_mul.Input("A"), "a");
+  ASSERT_EQ(grad_mul.Input("B"), "b");
+  ASSERT_EQ(grad_mul.Input("Out"), "out");
+}
+
+TEST(Backward, linear_net_intermediate_variable_has_no_grad) {
+  f::NetOp net;
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"x1", "w1", "b1"}, {"out1"}, {}));
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"out1", "w2", "b2"}, {"out2"}, {}));
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"out2", "w3", "b3"}, {"out3"}, {}));
+  net.CompleteAddOp(false);
+  auto backward = f::Backward(net, {"out2"});
+  ASSERT_TRUE(backward->IsNetOp());
+  auto bwd_net = static_cast<f::NetOp *>(backward.get());
+  ASSERT_EQ(bwd_net->ops_.size(), 1UL);
+
+  auto &grad_fc = *bwd_net->ops_[0];
+  ASSERT_EQ(grad_fc.type_, "fc_grad");
+  ASSERT_EQ(grad_fc.inputs_.size(), 3UL + 1UL + 1UL);
+  ASSERT_EQ(grad_fc.outputs_.size(), 3UL);
+  ASSERT_EQ(grad_fc.Output("X" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            f::OperatorBase::EMPTY_VAR_NAME());
+  ASSERT_EQ(grad_fc.Output("W" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            "w3" + f::OperatorBase::GRAD_VAR_SUFFIX());
+  ASSERT_EQ(grad_fc.Output("b" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            "b3" + f::OperatorBase::GRAD_VAR_SUFFIX());
+  ASSERT_EQ(grad_fc.Input("Out" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            "out3" + f::OperatorBase::GRAD_VAR_SUFFIX());
+  ASSERT_EQ(grad_fc.Input("X"), "out2");
+  ASSERT_EQ(grad_fc.Input("W"), "w3");
+  ASSERT_EQ(grad_fc.Input("b"), "b3");
+  ASSERT_EQ(grad_fc.Input("Out"), "out3");
 }
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