diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index 9830e4c09254e84bfc45234af14efcc4da513bb7..36d6cbb5eec8a22d3529a66dd6d2732ee156b026 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -154,7 +154,6 @@ REGISTER_OP(fill_zeros_like, f::EmptyOp, f::FillZeroOpMaker);
 REGISTER_OP(add, f::EmptyOp, f::AddOpMaker);
 REGISTER_GRADIENT_OP(add, add_grad, f::EmptyOp);
 REGISTER_OP(fc, f::FcOp, f::FcOpMaker);
-REGISTER_GRADIENT_OP(fc, fc_grad, f::EmptyOp);
 REGISTER_OP(many_output_op, f::EmptyOp, f::ManyOutputOpMaker);
 REGISTER_GRADIENT_OP(many_output_op, many_output_op_grad, f::EmptyOp);
 
@@ -326,7 +325,6 @@ TEST(Backward, op_part_of_output_are_not_need) {
             d_many_out.Output("x" + f::OperatorBase::GRAD_VAR_SUFFIX()));
 }
 
-/*
 TEST(Backward, op_part_of_input_are_not_need) {
   auto fwd = f::OpRegistry::CreateOp("mul", {"a", "b"}, {"out"}, {});
   auto backward = f::Backward(*fwd, {"a"});
@@ -344,7 +342,6 @@ TEST(Backward, op_part_of_input_are_not_need) {
   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;
@@ -359,13 +356,19 @@ TEST(Backward, linear_net_intermediate_variable_has_no_grad) {
   ASSERT_TRUE(backward->IsNetOp());
   auto bwd_net = static_cast<f::NetOp *>(backward.get());
   ASSERT_EQ(bwd_net->ops_.size(), 3UL);
-  EXPECT_EQ(bwd_net->ops_[0]->type_, "fc_grad");
+  EXPECT_EQ(bwd_net->ops_[0]->type_, "");
   EXPECT_EQ(bwd_net->ops_[1]->type_, "");
   EXPECT_EQ(bwd_net->ops_[2]->type_, "");
 
   auto &grad_fc = *bwd_net->ops_[0];
   EXPECT_EQ(grad_fc.inputs_.size(), 3UL + 3UL + 3UL);
   EXPECT_EQ(grad_fc.outputs_.size(), 3UL);
+
+  EXPECT_EQ(bwd_net->ops_[1]->inputs_.size(), 0UL);
+  EXPECT_EQ(bwd_net->ops_[1]->outputs_.size(), 0UL);
+  EXPECT_EQ(bwd_net->ops_[2]->inputs_.size(), 0UL);
+  EXPECT_EQ(bwd_net->ops_[2]->outputs_.size(), 0UL);
+
   EXPECT_EQ(grad_fc.Output("X" + f::OperatorBase::GRAD_VAR_SUFFIX()),
             f::OperatorBase::EMPTY_VAR_NAME());
   EXPECT_EQ(grad_fc.Output("W" + f::OperatorBase::GRAD_VAR_SUFFIX()),