diff --git a/paconvert/api_mapping.json b/paconvert/api_mapping.json
index 3f169ba4c..24051a16f 100644
--- a/paconvert/api_mapping.json
+++ b/paconvert/api_mapping.json
@@ -2834,6 +2834,107 @@
       "input": "x"
     }
   },
+  "torch.autograd.backward": {
+    "Matcher": "GenericMatcher",
+    "paddle_api": "paddle.autograd.backward",
+    "args_list": [
+      "tensors",
+      "grad_tensors",
+      "retain_graph",
+      "create_graph",
+      "grad_variables",
+      "inputs"
+    ],
+    "unsupport_args": [
+      "create_graph",
+      "grad_variables",
+      "inputs"
+    ]
+  },
+  "torch.autograd.functional.hessian": {
+    "Matcher": "GenericMatcher",
+    "paddle_api": "paddle.incubate.autograd.Hessian",
+    "args_list": [
+      "func",
+      "inputs",
+      "create_graph",
+      "strict",
+      "vectorize",
+      "outer_jacobian_strategy"
+    ],
+    "unsupport_args": [
+      "create_graph",
+      "strict",
+      "vectorize",
+      "outer_jacobian_strategy"
+    ],
+    "kwargs_change": {
+      "inputs": "xs"
+    },
+    "paddle_default_kwargs": {
+      "is_batched": false
+    }
+  },
+  "torch.autograd.functional.jacobian": {
+    "Matcher": "GenericMatcher",
+    "paddle_api": "paddle.incubate.autograd.Jacobian",
+    "args_list": [
+      "func",
+      "inputs",
+      "create_graph",
+      "strict",
+      "vectorize",
+      "strategy"
+    ],
+    "unsupport_args": [
+      "create_graph",
+      "strict",
+      "vectorize",
+      "strategy"
+    ],
+    "kwargs_change": {
+      "inputs": "xs"
+    },
+    "paddle_default_kwargs": {
+      "is_batched": false
+    }
+  },
+  "torch.autograd.functional.jvp": {
+    "Matcher": "GenericMatcher",
+    "paddle_api": "paddle.incubate.autograd.jvp",
+    "args_list": [
+      "func",
+      "inputs",
+      "v",
+      "create_graph",
+      "strict"
+    ],
+    "unsupport_args": [
+      "create_graph",
+      "strict"
+    ],
+    "kwargs_change": {
+      "inputs": "xs"
+    }
+  },
+  "torch.autograd.functional.vjp": {
+    "Matcher": "GenericMatcher",
+    "paddle_api": "paddle.incubate.autograd.vjp",
+    "args_list": [
+      "func",
+      "inputs",
+      "v",
+      "create_graph",
+      "strict"
+    ],
+    "unsupport_args": [
+      "create_graph",
+      "strict"
+    ],
+    "kwargs_change": {
+      "inputs": "xs"
+    }
+  },
   "torch.autograd.grad": {
     "Matcher": "GenericMatcher",
     "paddle_api": "paddle.grad",
diff --git a/tests/test_autograd_backward.py b/tests/test_autograd_backward.py
new file mode 100644
index 000000000..35972de59
--- /dev/null
+++ b/tests/test_autograd_backward.py
@@ -0,0 +1,77 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+
+import textwrap
+
+from apibase import APIBase
+
+obj = APIBase("torch.autograd.backward")
+
+
+def test_case_1():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32, requires_grad=True)
+        y = torch.tensor([[3, 2], [3, 4]], dtype=torch.float32)
+
+        grad_tensor1 = torch.tensor([[1,2], [2, 3]], dtype=torch.float32)
+        grad_tensor2 = torch.tensor([[1,1], [1, 1]], dtype=torch.float32)
+
+        z1 = torch.matmul(x, y)
+        z2 = torch.matmul(x, y)
+
+        torch.autograd.backward([z1, z2], [grad_tensor1, grad_tensor2], True)
+        x.grad.requires_grad=False
+        result = x.grad
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_2():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32, requires_grad=True)
+        y = torch.tensor([[3, 2], [3, 4]], dtype=torch.float32)
+
+        grad_tensor1 = torch.tensor([[1,2], [2, 3]], dtype=torch.float32)
+        grad_tensor2 = torch.tensor([[1,1], [1, 1]], dtype=torch.float32)
+
+        z1 = torch.matmul(x, y)
+        z2 = torch.matmul(x, y)
+
+        torch.autograd.backward([z1, z2], [grad_tensor1, grad_tensor2], retain_graph=False)
+        x.grad.requires_grad=False
+        result = x.grad
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_3():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32, requires_grad=True)
+        z1 = x.sum()
+
+        torch.autograd.backward([z1])
+        x.grad.requires_grad=False
+        result = x.grad
+        """
+    )
+    obj.run(pytorch_code, ["result"])
diff --git a/tests/test_autograd_functional_hessian.py b/tests/test_autograd_functional_hessian.py
new file mode 100644
index 000000000..dd481f2b8
--- /dev/null
+++ b/tests/test_autograd_functional_hessian.py
@@ -0,0 +1,70 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import textwrap
+
+from apibase import APIBase
+
+obj = APIBase("torch.autograd.functional.hessian")
+
+
+def test_case_1():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        def func(x):
+            return torch.sum(x * x)
+        x = torch.rand(2, 2)
+        h = torch.autograd.functional.hessian(func, x)
+        result = h[:]
+        result.requires_grad = False
+        result = torch.flatten(result)
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_2():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return 2 * torch.sum(x * x + 3 * x)
+
+        x = torch.rand(2, 2)
+        h = torch.autograd.functional.hessian(func, x)
+        result = h[:]
+        result.requires_grad = False
+        result = torch.flatten(result)
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_3():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return torch.sum(x)
+
+        x = torch.tensor([1.0, 2.0])
+        h = torch.autograd.functional.hessian(func, x)
+        result = h[:]
+        result.requires_grad = False
+        result = torch.flatten(result)
+        """
+    )
+    obj.run(pytorch_code, ["result"])
diff --git a/tests/test_autograd_functional_jacobian.py b/tests/test_autograd_functional_jacobian.py
new file mode 100644
index 000000000..9bac779ac
--- /dev/null
+++ b/tests/test_autograd_functional_jacobian.py
@@ -0,0 +1,69 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import textwrap
+
+from apibase import APIBase
+
+obj = APIBase("torch.autograd.functional.jacobian")
+
+
+def test_case_1():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return x * x
+
+        x = torch.tensor([1., 2.])
+        J = torch.autograd.functional.jacobian(func, x)
+        result = J[:]
+        result.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_2():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return torch.cos(x)
+
+        x = torch.tensor([1., 2.])
+        J = torch.autograd.functional.jacobian(func, x)
+        result = J[:]
+        result.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_3():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return torch.log(x)
+
+        x = torch.tensor([1., 2.])
+        J = torch.autograd.functional.jacobian(func, x)
+        result = J[:]
+        result.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
diff --git a/tests/test_autograd_functional_jvp.py b/tests/test_autograd_functional_jvp.py
new file mode 100644
index 000000000..3050ae22d
--- /dev/null
+++ b/tests/test_autograd_functional_jvp.py
@@ -0,0 +1,73 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import textwrap
+
+from apibase import APIBase
+
+obj = APIBase("torch.autograd.functional.jvp")
+
+
+def test_case_1():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        def func(x):
+            return torch.sum(x * x)
+        x = torch.ones(2, 3)
+        v = torch.ones(2, 3)
+        h = torch.autograd.functional.jvp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_2():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return 2 * torch.sum(x * x + 3 * x)
+
+        x = torch.arange(6, dtype=torch.float32).reshape(2, 3)
+        v = torch.ones(2, 3)
+        h = torch.autograd.functional.jvp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_3():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return torch.sum(x)
+
+        x = torch.tensor([1.0, 2.0])
+        v = torch.ones(2)
+        h = torch.autograd.functional.jvp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
diff --git a/tests/test_autograd_functional_vjp.py b/tests/test_autograd_functional_vjp.py
new file mode 100644
index 000000000..8139be63d
--- /dev/null
+++ b/tests/test_autograd_functional_vjp.py
@@ -0,0 +1,74 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import textwrap
+
+from apibase import APIBase
+
+obj = APIBase("torch.autograd.functional.vjp")
+
+
+def test_case_1():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+        def func(x):
+            return x.sum(dim=1)
+
+        x = torch.ones(2, 2)
+        v = torch.ones(2)
+        h = torch.autograd.functional.vjp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_2():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return x.sum(dim=1)
+
+        x = torch.arange(6, dtype=torch.float32).reshape(2, 3)
+        v = torch.ones(2)
+        h = torch.autograd.functional.vjp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])
+
+
+def test_case_3():
+    pytorch_code = textwrap.dedent(
+        """
+        import torch
+
+        def func(x):
+            return x * x
+
+        x = torch.tensor([1.0, 2.0])
+        v = torch.ones(2)
+        h = torch.autograd.functional.vjp(func, x, v)
+        result = h[:]
+        for item in result:
+            item.requires_grad = False
+        """
+    )
+    obj.run(pytorch_code, ["result"])