diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index 609dc661f2abcf9e892209501550292e8ed4fdb0..6ab81b5589307efe83f725537195671794cd6dcb 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -128,6 +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("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]);
@@ -138,6 +139,67 @@ TEST(Backward, simple_grad) {
   //  LOG(INFO) << gop->Output("X" + "@GRAD");
 }
 
+TEST(Backward, fc_backward_normal) {
+  std::shared_ptr<f::OperatorBase> fwd =
+      f::OpRegistry::CreateOp("fc", {"X", "w", "b"}, {"out"}, {});
+  ASSERT_NE(fwd, nullptr);
+  std::shared_ptr<f::OperatorBase> gop = f::Backward(*fwd, {});
+  ASSERT_TRUE(gop->IsNetOp());
+  auto net = static_cast<f::NetOp *>(gop.get());
+
+  ASSERT_NO_THROW(net->DebugString());
+
+  ASSERT_EQ(3UL, net->ops_.size());
+
+  f::OperatorBase &d_sigmoid = *net->ops_[0];
+  ASSERT_EQ("sigmoid_grad", d_sigmoid.type_);
+
+  f::OperatorBase &d_add = *net->ops_[1];
+  ASSERT_EQ("rowwise_add_grad", d_add.type_);
+
+  f::OperatorBase &d_mul = *net->ops_[2];
+  ASSERT_EQ("mul_grad", d_mul.type_);
+}
+
+TEST(Backward, fc_backward_not_have_b) {
+  std::shared_ptr<f::OperatorBase> fwd = f::OpRegistry::CreateOp(
+      "fc", {"X", "w", f::OperatorBase::EMPTY_VAR_NAME()}, {"out"}, {});
+  ASSERT_NE(fwd, nullptr);
+  std::shared_ptr<f::OperatorBase> gop = f::Backward(*fwd, {});
+  ASSERT_TRUE(gop->IsNetOp());
+  auto net = static_cast<f::NetOp *>(gop.get());
+
+  ASSERT_NO_THROW(net->DebugString());
+
+  ASSERT_EQ(2UL, net->ops_.size());
+
+  f::OperatorBase &d_sigmoid = *net->ops_[0];
+  ASSERT_EQ("sigmoid_grad", d_sigmoid.type_);
+
+  f::OperatorBase &d_mul = *net->ops_[1];
+  ASSERT_EQ("mul_grad", d_mul.type_);
+}
+
+TEST(Backward, input_layer_not_need_grad) {
+  f::NetOp net;
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"X", "W1", "b1"}, {"hidden0"}, {}));
+  net.AddOp(
+      f::OpRegistry::CreateOp("fc", {"hidden0", "W2", "b2"}, {"hidden1"}, {}));
+
+  auto bwd = Backward(net, {"X"});  // X@GRAD is not need.
+  ASSERT_TRUE(bwd->IsNetOp());
+  auto bwd_net = static_cast<f::NetOp *>(bwd.get());
+
+  std::unordered_set<std::string> all_output = std::unordered_set<std::string>(
+      bwd_net->outputs_.begin(), bwd_net->outputs_.end());
+  all_output.erase(f::OperatorBase::EMPTY_VAR_NAME());
+
+  for (auto &out : {"W1", "b1", "hidden0", "W2", "b2"}) {
+    ASSERT_NE(all_output.find(out + f::OperatorBase::GRAD_VAR_SUFFIX()),
+              all_output.end());
+  }
+}
+
 TEST(Backward, not_for_network) {
   auto fwd =
       f::OpRegistry::CreateOp("fc", {"X", "W", "b"}, {"Out", "tmp_out"},
@@ -166,7 +228,7 @@ TEST(Backward, part_of_output_are_not_need) {
   auto backward = f::Backward(*fwd, {"Z"});
   ASSERT_TRUE(backward->IsNetOp());
   auto net = static_cast<f::NetOp *>(backward.get());
-  ASSERT_EQ(net->ops_.size(), 2);
+  ASSERT_EQ(net->ops_.size(), 2UL);
 
   auto &fill_zero = *net->ops_[0];
   ASSERT_EQ("fill_zeros_like", fill_zero.type_);