diff --git a/python/paddle/fluid/tests/unittests/dygraph_to_static/test_cinn_prim_gelu.py b/python/paddle/fluid/tests/unittests/dygraph_to_static/test_cinn_prim_gelu.py
new file mode 100644
index 0000000000000000000000000000000000000000..bd8587b906778f3b876f518e65233793f2368b2b
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/dygraph_to_static/test_cinn_prim_gelu.py
@@ -0,0 +1,129 @@
+# 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 platform
+import unittest
+
+import numpy as np
+
+import paddle
+import paddle.nn.functional as F
+from paddle.fluid import core
+
+TOLERANCE = {
+    "float16": {"rtol": 1e-3, "atol": 1e-3},
+    "float32": {"rtol": 1e-6, "atol": 1e-6},
+    "float64": {"rtol": 1e-15, "atol": 1e-15},
+}
+
+approximate_conds = [True, False]
+
+
+def apply_to_static(net, use_cinn):
+    build_strategy = paddle.static.BuildStrategy()
+    build_strategy.build_cinn_pass = use_cinn
+    return paddle.jit.to_static(net, build_strategy=build_strategy)
+
+
+def generate_data(shape, dtype="float32"):
+    np_data = np.random.random(shape).astype(dtype)
+    return np_data
+
+
+class PrimeNet(paddle.nn.Layer):
+    def __init__(self, approximate):
+        super(PrimeNet, self).__init__()
+        self.fc = paddle.nn.Linear(4, 4)
+        self.approximate = approximate
+
+    def forward(self, x):
+        # y = self.fc(x)
+        out = F.gelu(x, approximate=self.approximate)
+        return out
+
+
+class TestPrimForwardAndBackward(unittest.TestCase):
+    """
+    Test PrimeNet with @to_static + prim forward + prim backward + cinn v.s Dygraph
+    """
+
+    def setUp(self):
+        paddle.seed(2022)
+        self.shapes = [[2, 4], [64, 16, 4]]
+        self.dtypes = ["float16", "float32"]
+
+    def train(self, use_prim, data):
+        for approximate in approximate_conds:
+            return self._train(use_prim, approximate, data)
+
+    def _train(self, use_prim, approximate, data):
+        paddle.seed(2022)
+        net = PrimeNet(approximate)
+        sgd = paddle.optimizer.SGD(
+            learning_rate=0.1, parameters=net.parameters()
+        )
+        core._set_prim_all_enabled(use_prim)
+        if use_prim:
+            net = apply_to_static(net, use_prim)
+
+        res = []
+        for _ in range(10):
+            out = net(data)
+            loss = paddle.mean(out)
+            loss.backward()
+            sgd.step()
+            sgd.clear_grad()
+
+            res.append(out.numpy())
+        self.check_prim(net, use_prim)
+
+        return res
+
+    def check_prim(self, net, use_prim):
+        if not use_prim:
+            return
+        fwd_ops = [op.type for op in net.forward.main_program.block(0).ops]
+        # Ensure that gelu is splitted into small ops
+        self.assertTrue('gelu' not in fwd_ops)
+
+    def test_cinn_prim(self):
+        plat = platform.system()
+        if plat == "Linux":
+            for shape in self.shapes:
+                for dtype in self.dtypes:
+                    if (
+                        paddle.device.get_device() == "cpu"
+                        and dtype == "float16"
+                    ):
+                        print("need pass this case")
+                        continue
+                    data = generate_data(shape, dtype)
+                    data_t = paddle.to_tensor(data)
+                    data_t.stop_gradient = False
+                    dy_res = self.train(use_prim=False, data=data_t)
+                    cinn_res = self.train(use_prim=True, data=data_t)
+                    for i in range(len(dy_res)):
+                        np.testing.assert_allclose(
+                            cinn_res[i],
+                            dy_res[i],
+                            rtol=TOLERANCE[dtype]['rtol'],
+                            atol=TOLERANCE[dtype]['atol'],
+                        )
+
+        else:
+            pass
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu.py b/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e5c10f803ae34bd542102a3b1c1f1be69940ba0
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu.py
@@ -0,0 +1,133 @@
+# Copyright (c) 2022 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 unittest
+
+import numpy as np
+from utils import TOLERANCE
+
+np.random.seed(2013)
+
+import paddle
+import paddle.nn.functional as F
+from paddle.fluid import core
+
+
+def generate_data(shape, dtype="float32"):
+    np_data = np.random.random(shape).astype(dtype)
+    return np_data
+
+
+class Attr:
+    def __init__(self) -> None:
+        self.dtype = "float32"
+        self.shape = None
+        self.approximate = False
+
+    def set_dtype(self, dtype) -> None:
+        self.dtype = dtype
+        return
+
+    def set_shape(self, shape) -> None:
+        self.shape = shape
+        return
+
+    def set_approximate(self, approximate) -> None:
+        self.approximate = approximate
+        return
+
+    def get_rtol(self, flag):
+        rtol = TOLERANCE[self.dtype][flag].get("rtol")
+        return rtol
+
+    def get_atol(self, flag):
+        atol = TOLERANCE[self.dtype][flag].get("atol")
+        return atol
+
+
+attrs = Attr()
+
+
+def fn(x):
+    return F.gelu(x, approximate=attrs.approximate)
+
+
+def expect_forward(inputs):
+    return fn(inputs)
+
+
+class TestCompositeGelu(unittest.TestCase):
+    def setUp(self):
+        self.dtypes = ["float16", "float32", "float64"]
+        self.shapes = [[16, 16, 64, 64], [2, 3, 4], [2, 3]]
+        self.approximate = [True, False]
+
+    def cal_composite(self, inputs):
+        paddle.enable_static()
+        core._set_prim_forward_enabled(True)
+        startup_program = paddle.static.Program()
+        main_program = paddle.static.Program()
+        with paddle.static.program_guard(main_program, startup_program):
+            x = paddle.static.data(
+                'x', shape=inputs.shape, dtype=str(inputs.dtype)
+            )
+            y = fn(x)
+            blocks = main_program.blocks
+
+            fwd_ops = [op.type for op in blocks[0].ops]
+            # Ensure that gelu in original block
+            self.assertTrue('gelu' in fwd_ops)
+
+            paddle.incubate.autograd.to_prim(blocks)
+
+            fwd_ops_new = [op.type for op in blocks[0].ops]
+            # Ensure that gelu is splitted into small ops
+            self.assertTrue('gelu' not in fwd_ops_new)
+
+        exe = paddle.static.Executor()
+        exe.run(startup_program)
+        res = exe.run(main_program, feed={'x': inputs}, fetch_list=[y])
+        paddle.disable_static()
+        return res
+
+    def compare_forward(self):
+        np_data = generate_data(attrs.shape, attrs.dtype)
+        tensor_data = paddle.to_tensor(np_data)
+
+        expect = expect_forward(tensor_data).numpy()
+        actual = self.cal_composite(np_data)[0]
+        assert expect.dtype == actual.dtype
+        np.testing.assert_allclose(
+            expect,
+            actual,
+            rtol=attrs.get_rtol("forward"),
+            atol=attrs.get_atol("forward"),
+        )
+
+    def test_forward(self):
+        for i in self.approximate:
+            for j in self.dtypes:
+                for t in self.shapes:
+                    # gelu-kernel on cpu not support float16
+                    if paddle.device.get_device() == "cpu" and j == "float16":
+                        print("need pass this case")
+                        continue
+                    attrs.set_approximate(i)
+                    attrs.set_dtype(j)
+                    attrs.set_shape(t)
+                    self.compare_forward()
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu_grad.py b/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu_grad.py
new file mode 100644
index 0000000000000000000000000000000000000000..dda900e2472723e5c52d48f79342734902c2eac5
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/prim/composite_ops/test_composite_gelu_grad.py
@@ -0,0 +1,205 @@
+# Copyright (c) 2022 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 unittest
+
+import numpy as np
+from utils import TOLERANCE
+
+np.random.seed(2013)
+
+import paddle
+import paddle.nn.functional as F
+from paddle.fluid import core
+
+
+def generate_data(shape, dtype="float32"):
+    np_data = np.random.random(shape).astype(dtype)
+    return np_data
+
+
+class Attr:
+    def __init__(self) -> None:
+        self.dtype = "float32"
+        self.shape = None
+        self.approximate = False
+
+    def set_dtype(self, dtype) -> None:
+        self.dtype = dtype
+        return
+
+    def set_shape(self, shape) -> None:
+        self.shape = shape
+        return
+
+    def set_approximate(self, approximate) -> None:
+        self.approximate = approximate
+        return
+
+    def get_rtol(self, flag):
+        rtol = TOLERANCE[self.dtype][flag].get("rtol")
+        return rtol
+
+    def get_atol(self, flag):
+        atol = TOLERANCE[self.dtype][flag].get("atol")
+        return atol
+
+
+attrs = Attr()
+
+
+def fn(x):
+    return F.gelu(x, approximate=attrs.approximate)
+
+
+def expect_grad(inputs):
+    paddle.disable_static()
+    inputs.stop_gradient = False
+    res = fn(inputs)
+
+    gradients = paddle.grad(res, inputs)
+    return gradients
+
+
+class TestCompositeGelu(unittest.TestCase):
+    "test composite gelu: prim forward"
+
+    def setUp(self):
+        self.dtypes = ["float16", "float32", "float64"]
+        self.shapes = [[16, 16, 64, 64], [2, 3, 4], [2, 3]]
+        self.approximates = [True, False]
+
+    def cal_composite_grad(self, inputs):
+        paddle.enable_static()
+        core._set_prim_forward_enabled(True)
+        startup_program = paddle.static.Program()
+        main_program = paddle.static.Program()
+        with paddle.static.program_guard(main_program, startup_program):
+            x = paddle.static.data(
+                'x', shape=inputs.shape, dtype=str(inputs.dtype)
+            )
+            x.stop_gradient = False
+            y = fn(x)
+            blocks = main_program.blocks
+
+            fwd_ops = [op.type for op in blocks[0].ops]
+            # Ensure that gelu in original block
+            self.assertTrue('gelu' in fwd_ops)
+
+            paddle.incubate.autograd.to_prim(blocks)
+
+            fwd_ops_new = [op.type for op in blocks[0].ops]
+            # Ensure that gelu is splitted into small ops
+            self.assertTrue('gelu' not in fwd_ops_new)
+
+            z = paddle.static.gradients([y], x)
+            fwd_ops_grad = [op.type for op in blocks[0].ops]
+            # Ensure that gelu_grad not in grad block
+
+            self.assertTrue('gelu_grad' not in fwd_ops_grad)
+
+        exe = paddle.static.Executor()
+        exe.run(startup_program)
+        res = exe.run(main_program, feed={'x': inputs}, fetch_list=[z])
+        paddle.disable_static()
+        core._set_prim_forward_enabled(False)
+        return res
+
+    def compare_backward(self):
+        np_data = generate_data(attrs.shape, attrs.dtype)
+        tensor_data = paddle.to_tensor(np_data)
+
+        expect = expect_grad(tensor_data)[0].numpy()
+        actual = self.cal_composite_grad(np_data)[0]
+
+        assert expect.dtype == actual.dtype
+        np.testing.assert_allclose(
+            expect,
+            actual,
+            rtol=attrs.get_rtol("backward"),
+            atol=attrs.get_atol("backward"),
+        )
+
+    def test_backward(self):
+        for i in self.approximates:
+            for j in self.dtypes:
+                for t in self.shapes:
+                    if paddle.device.get_device() == "cpu" and j == "float16":
+                        print("need pass this case")
+                        continue
+                    attrs.set_approximate(i)
+                    attrs.set_dtype(j)
+                    attrs.set_shape(t)
+                    self.compare_backward()
+
+
+class TestCompositeGeluPrimBackward(unittest.TestCase):
+    "test composite gelu: prim forward and backward"
+
+    def setUp(self):
+        self.dtypes = ["float16", "float32", "float64"]
+        self.shapes = [[16, 16, 64, 64], [2, 3, 4], [2, 3]]
+        self.approximates = [True, False]
+
+    def cal_composite_grad(self, inputs):
+        paddle.enable_static()
+        core._set_prim_all_enabled(True)
+        startup_program = paddle.static.Program()
+        main_program = paddle.static.Program()
+        with paddle.static.program_guard(main_program, startup_program):
+            x = paddle.static.data(
+                'x', shape=inputs.shape, dtype=str(inputs.dtype)
+            )
+            x.stop_gradient = False
+            y = fn(x)
+            blocks = main_program.blocks
+            paddle.incubate.autograd.to_prim(blocks)
+            z = paddle.static.gradients([y], x)
+
+        exe = paddle.static.Executor()
+        exe.run(startup_program)
+        res = exe.run(main_program, feed={'x': inputs}, fetch_list=[z])
+        paddle.disable_static()
+        core._set_prim_all_enabled(False)
+        return res
+
+    def compare_backward(self):
+        np_data = generate_data(attrs.shape, attrs.dtype)
+        tensor_data = paddle.to_tensor(np_data)
+        expect = expect_grad(tensor_data)[0].numpy()
+        actual = self.cal_composite_grad(np_data)[0]
+
+        assert expect.dtype == actual.dtype
+        np.testing.assert_allclose(
+            expect,
+            actual,
+            rtol=attrs.get_rtol("prim_backward"),
+            atol=attrs.get_rtol("prim_backward"),
+        )
+
+    def test_prim_backward(self):
+        for i in self.approximates:
+            for j in self.dtypes:
+                for t in self.shapes:
+                    if paddle.device.get_device() == "cpu" and j == "float16":
+                        print("need pass this case")
+                        continue
+                    attrs.set_approximate(i)
+                    attrs.set_dtype(j)
+                    attrs.set_shape(t)
+                    self.compare_backward()
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/prim/composite_ops/utils.py b/python/paddle/fluid/tests/unittests/prim/composite_ops/utils.py
index ed2365adf7c4f48d10afd3fc3e0c8e1db480afca..32358375f05d219f11b86d8fd5a8d02687930bab 100644
--- a/python/paddle/fluid/tests/unittests/prim/composite_ops/utils.py
+++ b/python/paddle/fluid/tests/unittests/prim/composite_ops/utils.py
@@ -14,6 +14,11 @@
 
 # default tolerance
 TOLERANCE = {
+    "float16": {
+        "forward": {"rtol": 1e-3, "atol": 1e-3},
+        "backward": {"rtol": 1e-3, "atol": 1e-3},
+        "prim_backward": {"rtol": 1e-3, "atol": 1e-3},
+    },
     "float32": {
         "forward": {"rtol": 1e-6, "atol": 1e-6},
         "backward": {"rtol": 1e-6, "atol": 1e-6},
diff --git a/python/paddle/incubate/autograd/composite_rules.py b/python/paddle/incubate/autograd/composite_rules.py
index d7eb54ba571974b7a127a674546bd347264ef2b0..bcf7ab2a4a4cd8b098f9bcd76b6b7c32c5e3c6ca 100644
--- a/python/paddle/incubate/autograd/composite_rules.py
+++ b/python/paddle/incubate/autograd/composite_rules.py
@@ -101,3 +101,27 @@ def composite_batchnorm(
         return run_mean_, None, batch_mean_, batch_var_, run_var_, y
     else:
         return run_mean_, batch_mean_, batch_var_, run_var_, y
+
+
+@REGISTER_COMPOSITE('gelu')
+def gelu_composite(x, approximate):
+    """define composite rule of op gelu"""
+    M_SQRT1_2 = (
+        0.70710678118654752440  # /* 1/sqrt(2) */ copy from gelu-kernel.cc
+    )
+    M_2_SQRTPI = 1.12837916709551257390  # /* 2/sqrt(pi) */
+    one = ones(x.shape, x.dtype)
+    half = full(x.shape, 0.5, x.dtype)
+    if approximate:
+        # gelu(x) = 0.5 * x * (1 + tanh(sqrt(2 / \pi) * (x + 0.044715 * x^{3})))
+        kAlpha = full(x.shape, M_2_SQRTPI * M_SQRT1_2, x.dtype)
+        GELU_CONSTANT = full(x.shape, 0.044715, x.dtype)
+        tanh_out = tanh(kAlpha * (x + GELU_CONSTANT * x * x * x))
+        out = x * half * (one + tanh_out)
+        return out
+
+    else:
+        # gelu(x) = 0.5 * x *  (1 + erf(x / sqrt(2)))
+        cdf = half * (one + erf(x * full(x.shape, M_SQRT1_2, x.dtype)))
+        out = x * cdf
+        return out
diff --git a/python/paddle/incubate/autograd/primitives.py b/python/paddle/incubate/autograd/primitives.py
index 3eb3ce5d0838965b7d2c9cd88d3e9ea20e0ddad5..35687279affda7037dddbecd336ae2ebd70c5b08 100644
--- a/python/paddle/incubate/autograd/primitives.py
+++ b/python/paddle/incubate/autograd/primitives.py
@@ -34,6 +34,7 @@ from paddle.tensor import erf  # noqa: F401
 from paddle.tensor import erfinv  # noqa: F401
 from paddle.tensor import exp  # noqa: F401
 from paddle.tensor import expm1  # noqa: F401
+from paddle.tensor import full  # noqa: F401
 from paddle.tensor import lgamma  # noqa: F401
 from paddle.tensor import log  # noqa: F401
 from paddle.tensor import log1p  # noqa: F401
@@ -113,6 +114,7 @@ others = [
     'assign',
     'fill_constant',
     'reshape',
+    'full',
 ]
 
 __all__ = []