diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index cb1d402526e0b0008263c8f19e4d175c6e1502f6..a481cb1b2a7ccfd41e5e07265b4809c53649e634 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -13,6 +13,7 @@
    limitations under the License. */
 
 #include "paddle/framework/backward.h"
+
 #include <gtest/gtest.h>
 #include "paddle/framework/net.h"
 #include "paddle/framework/op_registry.h"
@@ -161,12 +162,23 @@ TEST(Backward, simple_op_grad) {
 }
 
 TEST(Backward, simple_op_not_need_grad) {
-  auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"x", "b"}, {"out"}, {});
+  auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"X", "b"}, {"Out"}, {});
   ASSERT_NE(fwd, nullptr);
-  auto gop = f::Backward(*fwd, {"x"});
-  LOG(INFO) << gop->DebugString();
-  ASSERT_NE(gop->outputs_.find("x" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+  auto gop = f::Backward(*fwd, {"X"});
+  LOG(INFO) << "full " << gop->DebugString();
+  ASSERT_NE(std::find(gop->outputs_.begin(), gop->outputs_.end(),
+                      "X" + f::OperatorBase::GRAD_VAR_SUFFIX()),
             gop->outputs_.end());
+  auto no_input_gop = f::Backward(*fwd, {"X", "b"});
+  LOG(INFO) << "no input gop " << no_input_gop->DebugString();
+  ASSERT_NE(no_input_gop, nullptr);
+  ASSERT_EQ(std::vector<std::string>{}, no_input_gop->outputs_);
+  ASSERT_EQ(
+      std::vector<std::string>{"Out" + f::OperatorBase::GRAD_VAR_SUFFIX()},
+      no_input_gop->inputs_);
+  // auto no_output_gop = f::Backward(*fwd, {"Out"});
+  // ASSERT_EQ(std::vector<std::string>{"X" +
+  // f::OperatorBase::GRAD_VAR_SUFFIX(), "b"})
 }
 
 TEST(Backward, net_fc_backward_normal) {