diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index e920af3d1ac511f360ba32630c7812a939c27428..538522bf441ab71be6e76505e282a86b3878f267 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -128,7 +128,7 @@ TEST(Backward, simple_grad) {
   auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"X", "b"}, {"Out"}, {});
   ASSERT_NE(fwd, nullptr);
   auto gop = f::OpRegistry::CreateGradOp(*fwd);
-  ASSERT_EQ(1, gop->inputs_.size());
+  ASSERT_EQ(1UL, gop->inputs_.size());
   ASSERT_EQ("Out" + f::OperatorBase::GRAD_VAR_SUFFIX(), gop->inputs_[0]);
   ASSERT_EQ("rowwise_add_grad", gop->type_);
   ASSERT_EQ("X" + f::OperatorBase::GRAD_VAR_SUFFIX(), gop->outputs_[0]);
@@ -265,4 +265,36 @@ TEST(Backward, 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, intermediate_variable_not_need_in_linear_net) {
+  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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