diff --git a/paddle/phi/kernels/gpu/add_n_kernel.cu b/paddle/phi/kernels/gpu/add_n_kernel.cu
index 69bc248a7e2f2c87b9e90d14e22e6f6496bc3223..8bf3591f13c4c7a8b35bbed8cb4ee1f192dafe8c 100644
--- a/paddle/phi/kernels/gpu/add_n_kernel.cu
+++ b/paddle/phi/kernels/gpu/add_n_kernel.cu
@@ -75,6 +75,13 @@ void AddNKernel(const Context &dev_ctx,
                 const std::vector<const TensorBase *> &x,
                 DenseTensor *out) {
   const size_t in_num = x.size();
+  for (int i = 0; i < in_num; ++i) {
+    PADDLE_ENFORCE_EQ(
+        x[i]->initialized(),
+        true,
+        phi::errors::InvalidArgument(
+            "This argument is invalid, %d-th tensor is uninitialized.", i));
+  }
 
   constexpr size_t theory_sm_threads = 1024;
   auto stream = dev_ctx.stream();
diff --git a/python/paddle/fluid/backward.py b/python/paddle/fluid/backward.py
index 1ba11e1fba4c3fecfa9d9e20594bf039ffe50d3a..f3bc2635c4fbcda3139973fa21b2ad804be9705f 100755
--- a/python/paddle/fluid/backward.py
+++ b/python/paddle/fluid/backward.py
@@ -1672,6 +1672,18 @@ def _append_backward_vars_(block, start_op_idx, grad_to_var, grad_info_map):
                         ops_to_remove.append(op_idx)
                         continue
 
+        # sum may create invalid variable, here to deal with it.
+        if op_desc.type() == 'sum':
+            new_inputs = []
+            for grad_var_name in op_desc.input_arg_names():
+                if block.desc.has_var_recursive(grad_var_name.encode()):
+                    # meet invalid sum variables, remove the invalid operand.
+                    new_inputs.append(grad_var_name)
+            assert (
+                len(new_inputs) > 0
+            ), "After remove invalid variables, sum op have no inputs."
+            op_desc.set_input("X", new_inputs)
+
         new_vars = set()
         # create new gradient variables
         for grad_var_name in op_desc.output_arg_names():
diff --git a/python/paddle/fluid/tests/unittests/test_backward.py b/python/paddle/fluid/tests/unittests/test_backward.py
index 750732eb5d90794401938759b8738331fb7ebb88..c3d44d7b343c5a9c2c053de8e3747211bbabab24 100644
--- a/python/paddle/fluid/tests/unittests/test_backward.py
+++ b/python/paddle/fluid/tests/unittests/test_backward.py
@@ -409,6 +409,39 @@ class ConditionalNet(BackwardNet):
         super().__init__()
 
 
+class TestBackwardUninitializedVariable(unittest.TestCase):
+    """this case is found in yolov5 while to_static.
+    gradient aggregation may cause sum a invalid variable.
+    """
+
+    def test(self):
+        paddle.enable_static()
+        main_prg, startup_prg = paddle.static.Program(), paddle.static.Program()
+        with paddle.static.program_guard(main_prg, startup_prg):
+            gt = paddle.static.data(name='gt', shape=[4], dtype='float32')
+            x = paddle.static.data(name='x', shape=[2], dtype='float32')
+            gt.stop_gradient = True
+            x.stop_gradient = False
+            gt = gt.reshape([4, 1]).reshape([4])
+            loss = (
+                paddle.nn.functional.binary_cross_entropy(x, gt[:2])
+                + (gt[2:4] * x).sum()
+            )
+            exe = paddle.static.Executor()
+            paddle.fluid.backward.gradients(loss, [])
+            exe.run(startup_prg)
+            # Optimizer
+            out = exe.run(
+                main_prg,
+                feed={
+                    'gt': np.array([1.0, 1.0, 0.0, 0.0], dtype='float32'),
+                    'x': np.array([0.5, 0.5], dtype='float32'),
+                },
+                fetch_list=[loss],
+            )
+            print(out)
+
+
 if __name__ == '__main__':
     paddle.enable_static()
     unittest.main()