diff --git a/paddle/phi/kernels/cpu/fold_grad_kernel.cc b/paddle/phi/kernels/cpu/fold_grad_kernel.cc
index 0c3f1dda03e5e..a56b0aa054571 100644
--- a/paddle/phi/kernels/cpu/fold_grad_kernel.cc
+++ b/paddle/phi/kernels/cpu/fold_grad_kernel.cc
@@ -18,5 +18,11 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/impl/fold_grad_kernel_impl.h"
 
-PD_REGISTER_KERNEL(
-    fold_grad, CPU, ALL_LAYOUT, phi::FoldGradKernel, float, double) {}
+PD_REGISTER_KERNEL(fold_grad,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::FoldGradKernel,
+                   float,
+                   double,
+                   phi::dtype::complex<float>,
+                   phi::dtype::complex<double>) {}
diff --git a/paddle/phi/kernels/cpu/fold_kernel.cc b/paddle/phi/kernels/cpu/fold_kernel.cc
index e22ac4c771ed9..df6cf5652c992 100644
--- a/paddle/phi/kernels/cpu/fold_kernel.cc
+++ b/paddle/phi/kernels/cpu/fold_kernel.cc
@@ -18,4 +18,11 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/impl/fold_kernel_impl.h"
 
-PD_REGISTER_KERNEL(fold, CPU, ALL_LAYOUT, phi::FoldKernel, float, double) {}
+PD_REGISTER_KERNEL(fold,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::FoldKernel,
+                   float,
+                   double,
+                   phi::dtype::complex<float>,
+                   phi::dtype::complex<double>) {}
diff --git a/paddle/phi/kernels/funcs/im2col.cc b/paddle/phi/kernels/funcs/im2col.cc
index 0b5901367488a..e4c470e1a7064 100644
--- a/paddle/phi/kernels/funcs/im2col.cc
+++ b/paddle/phi/kernels/funcs/im2col.cc
@@ -160,12 +160,24 @@ template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
 template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
                              phi::CPUContext,
                              double>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::CPUContext,
+                             phi::dtype::complex<float>>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::CPUContext,
+                             phi::dtype::complex<double>>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
                              phi::CPUContext,
                              float>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
                              phi::CPUContext,
                              double>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::CPUContext,
+                             phi::dtype::complex<float>>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::CPUContext,
+                             phi::dtype::complex<double>>;
 
 /*
  * im = [input_channels, input_height, input_width]
@@ -331,11 +343,23 @@ template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
 template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
                              phi::CPUContext,
                              double>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::CPUContext,
+                             phi::dtype::complex<float>>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::CPUContext,
+                             phi::dtype::complex<double>>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
                              phi::CPUContext,
                              float>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
                              phi::CPUContext,
                              double>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::CPUContext,
+                             phi::dtype::complex<float>>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::CPUContext,
+                             phi::dtype::complex<double>>;
 }  // namespace funcs
 }  // namespace phi
diff --git a/paddle/phi/kernels/funcs/im2col.cu b/paddle/phi/kernels/funcs/im2col.cu
index 87c82adbb7fbe..b633241810f9b 100644
--- a/paddle/phi/kernels/funcs/im2col.cu
+++ b/paddle/phi/kernels/funcs/im2col.cu
@@ -310,6 +310,12 @@ template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
 template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
                              phi::GPUContext,
                              double>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::GPUContext,
+                             phi::dtype::complex<float>>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::GPUContext,
+                             phi::dtype::complex<double>>;
 template class Im2ColFunctor<phi::funcs::ColFormat::kCFO,
                              phi::GPUContext,
                              phi::dtype::float16>;
@@ -322,6 +328,12 @@ template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
 template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
                              phi::GPUContext,
                              double>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::GPUContext,
+                             phi::dtype::complex<float>>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
+                             phi::GPUContext,
+                             phi::dtype::complex<double>>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kCFO,
                              phi::GPUContext,
                              phi::dtype::float16>;
@@ -573,6 +585,12 @@ template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
 template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
                              phi::GPUContext,
                              double>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::GPUContext,
+                             phi::dtype::complex<float>>;
+template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::GPUContext,
+                             phi::dtype::complex<double>>;
 template class Im2ColFunctor<phi::funcs::ColFormat::kOCF,
                              phi::GPUContext,
                              phi::dtype::float16>;
@@ -585,6 +603,12 @@ template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
 template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
                              phi::GPUContext,
                              double>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::GPUContext,
+                             phi::dtype::complex<float>>;
+template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
+                             phi::GPUContext,
+                             phi::dtype::complex<double>>;
 template class Col2ImFunctor<phi::funcs::ColFormat::kOCF,
                              phi::GPUContext,
                              phi::dtype::float16>;
diff --git a/paddle/phi/kernels/gpu/fold_grad_kernel.cu b/paddle/phi/kernels/gpu/fold_grad_kernel.cu
index ad469dd7981de..1e3cceb04dd0d 100644
--- a/paddle/phi/kernels/gpu/fold_grad_kernel.cu
+++ b/paddle/phi/kernels/gpu/fold_grad_kernel.cu
@@ -18,5 +18,11 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/impl/fold_grad_kernel_impl.h"
 
-PD_REGISTER_KERNEL(
-    fold_grad, GPU, ALL_LAYOUT, phi::FoldGradKernel, float, double) {}
+PD_REGISTER_KERNEL(fold_grad,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::FoldGradKernel,
+                   float,
+                   double,
+                   phi::dtype::complex<float>,
+                   phi::dtype::complex<double>) {}
diff --git a/paddle/phi/kernels/gpu/fold_kernel.cu b/paddle/phi/kernels/gpu/fold_kernel.cu
index b53ef402150c2..2e21a121a0cc6 100644
--- a/paddle/phi/kernels/gpu/fold_kernel.cu
+++ b/paddle/phi/kernels/gpu/fold_kernel.cu
@@ -18,4 +18,11 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/impl/fold_kernel_impl.h"
 
-PD_REGISTER_KERNEL(fold, GPU, ALL_LAYOUT, phi::FoldKernel, float, double) {}
+PD_REGISTER_KERNEL(fold,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::FoldKernel,
+                   float,
+                   double,
+                   phi::dtype::complex<float>,
+                   phi::dtype::complex<double>) {}
diff --git a/python/paddle/nn/functional/common.py b/python/paddle/nn/functional/common.py
index bc43e73c4163d..1a23e072bd82b 100644
--- a/python/paddle/nn/functional/common.py
+++ b/python/paddle/nn/functional/common.py
@@ -2280,7 +2280,7 @@ def fold(
 
     Parameters:
         x(Tensor):                3-D Tensor, input tensor of format [N, C, L],
-                                  data type can be float32 or float64
+                                  data type can be float32, float64, complex64 or complex128
         output_sizes(int|list|tuple):       The size of output size, should be [output_size_h, output_size_w]
                                   or an interger o treated as [o, o].
         kernel_sizes(int|list|tuple):   The size of convolution kernel, should be [k_h, k_w]
@@ -2325,7 +2325,9 @@ def fold(
 
     helper = LayerHelper("fold", **locals())
 
-    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'fold')
+    check_variable_and_dtype(
+        x, 'x', ['float32', 'float64', 'complex64', 'complex128'], 'fold'
+    )
 
     assert len(x.shape) == 3, "input should be the format of [N, C, L]"
 
diff --git a/test/legacy_test/test_fold_op.py b/test/legacy_test/test_fold_op.py
index 8fdb37deadf21..2a8649b8a3a63 100644
--- a/test/legacy_test/test_fold_op.py
+++ b/test/legacy_test/test_fold_op.py
@@ -39,7 +39,15 @@ def init_data(self):
         self.dilations = [1, 1]
         self.output_sizes = [4, 5]
         input_shape = [self.batch_size, self.input_channels, self.length]
-        self.x = np.random.rand(*input_shape).astype(np.float64)
+        self.x = np.random.rand(*input_shape).astype(self.dtype)
+        if self.dtype == np.complex64 or self.dtype == np.complex128:
+            self.x = (
+                np.random.uniform(-1, 1, input_shape)
+                + 1j * np.random.uniform(-1, 1, input_shape)
+            ).astype(self.dtype)
+
+    def init_dtype(self):
+        self.dtype = np.float64
 
     def calc_fold(self):
         output_shape = [0] * 4
@@ -75,7 +83,7 @@ def calc_fold(self):
             )
             + 1
         )
-        output = np.zeros(output_shape).astype(np.float64)
+        output = np.zeros(output_shape).astype(self.dtype)
         # ------------- calculate output ------------- #
         for b in range(output_shape[0]):
             for c in range(self.input_channels):
@@ -106,6 +114,7 @@ def calc_fold(self):
         self.outputs = output
 
     def set_data(self):
+        self.init_dtype()
         self.init_data()
         self.calc_fold()
         self.inputs = {'X': OpTest.np_dtype_to_fluid_dtype(self.x)}
@@ -130,6 +139,16 @@ def test_check_grad(self):
         self.check_grad(['X'], 'Y')
 
 
+class TestFold_Complex64(TestFoldOp):
+    def init_dtype(self):
+        self.dtype = np.complex64
+
+
+class TestFold_Complex128(TestFoldOp):
+    def init_dtype(self):
+        self.dtype = np.complex128
+
+
 class TestFoldshape(TestFoldOp):
     def init_data(self):
         self.batch_size = 8