diff --git a/paddle/fluid/prim/api/composite_backward/composite_backward_api.h b/paddle/fluid/prim/api/composite_backward/composite_backward_api.h
index 823a068dcd78b47bfd6d82e6a215877152101db6..2fe33c92ff8c32284d8ae6bc0b79c932b249e422 100644
--- a/paddle/fluid/prim/api/composite_backward/composite_backward_api.h
+++ b/paddle/fluid/prim/api/composite_backward/composite_backward_api.h
@@ -14,6 +14,12 @@
 
 #pragma once
 
+#ifndef _USE_MATH_DEFINES
+#define _USE_MATH_DEFINES
+#endif
+
+#include <math.h>
+
 #include "paddle/fluid/prim/api/all.h"
 #include "paddle/fluid/prim/api/generated_prim/prim_generated_api.h"
 #include "paddle/phi/common/int_array.h"
@@ -881,5 +887,16 @@ void gather_nd_grad(const Tensor& x,
   }
 }
 
+template <typename T>
+void erf_grad(const Tensor& x, const Tensor& out_grad, Tensor* x_grad) {
+  if (x_grad) {
+    auto m_2_sqrt_pi = full<T>(phi::vectorize(x.dims()), M_2_SQRTPI, x.dtype());
+    auto neg_one = full<T>(phi::vectorize(x.dims()), -1.0, x.dtype());
+    auto neg_tmp = neg_one * x * x;
+    auto mul_tmp = m_2_sqrt_pi * exp<T>(neg_tmp);
+    set_output<T>(out_grad * mul_tmp, x_grad);
+  }
+}
+
 }  // namespace prim
 }  // namespace paddle
diff --git a/paddle/phi/api/yaml/backward.yaml b/paddle/phi/api/yaml/backward.yaml
index 4a42799764fa8014d06d0d4b6e0c84029bad258c..6108fbb5081ab6f5829e66bab8bbab5b92a2bf97 100644
--- a/paddle/phi/api/yaml/backward.yaml
+++ b/paddle/phi/api/yaml/backward.yaml
@@ -423,6 +423,7 @@
   kernel :
     func : erf_grad
     data_type : out_grad
+  composite : erf_grad(x, out_grad, x_grad)
 
 - backward_op : erfinv_grad
   forward : erfinv (Tensor x) -> Tensor(out)
diff --git a/python/paddle/fluid/tests/unittests/test_erf_op.py b/python/paddle/fluid/tests/unittests/test_erf_op.py
index db5c48151c5052e83be61912ad7368b734c79aba..0d78457b1452a52632d99158ff59560dd83a7690 100644
--- a/python/paddle/fluid/tests/unittests/test_erf_op.py
+++ b/python/paddle/fluid/tests/unittests/test_erf_op.py
@@ -26,6 +26,8 @@ import paddle.fluid.dygraph as dg
 class TestErfOp(OpTest):
     def setUp(self):
         self.op_type = "erf"
+        self.prim_op_type = "prim"
+        self.enable_cinn = True
         self.python_api = paddle.erf
         self.dtype = self._init_dtype()
         self.x_shape = [11, 17]
@@ -41,7 +43,7 @@ class TestErfOp(OpTest):
         self.check_output()
 
     def test_check_grad(self):
-        self.check_grad(['X'], 'Out')
+        self.check_grad(['X'], 'Out', check_prim=True)
 
 
 class TestErfLayer(unittest.TestCase):