diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index dd0d2be6685ce794372291caac3c541a6a5b9be2..878d3010deda5ab24468e86b4f06580c649e147a 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -166,7 +166,7 @@ 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_);
@@ -184,4 +184,23 @@ TEST(Backward, part_of_output_are_not_need) {
             d_many_out.Input("y" + f::OperatorBase::GRAD_VAR_SUFFIX()));
   ASSERT_EQ("X" + f::OperatorBase::GRAD_VAR_SUFFIX(),
             d_many_out.Output("x" + f::OperatorBase::GRAD_VAR_SUFFIX()));
+}
+
+TEST(Backward, part_of_input_are_not_need) {
+  auto fwd = f::OpRegistry::CreateOp("mul", {"a", "b"}, {"out"}, {});
+  auto backward = f::Backward(*fwd, {"a"});
+  ASSERT_TRUE(backward->IsNetOp());
+  auto net = static_cast<f::NetOp *>(backward.get());
+  ASSERT_EQ(net->ops_.size(), 1UL);
+
+  auto &grad_mul = *net->ops_[0];
+  ASSERT_EQ(grad_mul.type_, "mul_grad");
+  ASSERT_EQ(grad_mul.inputs_.size(), 2UL + 1UL + 1UL);
+  ASSERT_EQ(grad_mul.outputs_.size(), 2UL);
+  ASSERT_EQ(grad_mul.Output("A" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            f::OperatorBase::EMPTY_VAR_NAME());
+  ASSERT_EQ(grad_mul.Output("B" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            "b" + f::OperatorBase::GRAD_VAR_SUFFIX());
+  ASSERT_EQ(grad_mul.Input("Out" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            "out" + f::OperatorBase::GRAD_VAR_SUFFIX());
 }
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