diff --git a/paddle/fluid/distributed/ps/table/depends/initializers.h b/paddle/fluid/distributed/ps/table/depends/initializers.h
index 5ac0c08f97d76f6bc1cb77f1f6cd0da77be2385f..f46e659a88babb07918d02f1e05859829895f2bf 100644
--- a/paddle/fluid/distributed/ps/table/depends/initializers.h
+++ b/paddle/fluid/distributed/ps/table/depends/initializers.h
@@ -23,6 +23,7 @@
 #include "gflags/gflags.h"
 
 #include "paddle/fluid/framework/generator.h"
+
 #include "paddle/fluid/operators/truncated_gaussian_random_op.h"
 
 namespace paddle {
@@ -117,13 +118,9 @@ class TruncatedGaussianInitializer : public Initializer {
     seed_ = static_cast<unsigned int>(std::stoi(attrs[1]));
     mean_ = std::stof(attrs[2]);
     std_ = std::stof(attrs[3]);
-    auto normal_cdf = [](float x) {
-      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-    };
-    float a_normal_cdf = normal_cdf((-2.0 - mean_) / std_);
-    float b_normal_cdf = normal_cdf((2.0 - mean_) / std_);
-    std::uniform_real_distribution<float> dist_(2.0 * a_normal_cdf - 1.0,
-                                                2.0 * b_normal_cdf - 1.0);
+
+    std::uniform_real_distribution<float> dist_(
+        std::numeric_limits<float>::min(), 1.0);
     random_engine_ = framework::GetCPURandomEngine(seed_);
   }
 
diff --git a/paddle/fluid/operators/truncated_gaussian_random_op.h b/paddle/fluid/operators/truncated_gaussian_random_op.h
index 8af6e281424eaabd8d6ea86843b3c13aa36cba47..a6ff2f686cb76bb03de8074014f82d6ff9e57bd3 100644
--- a/paddle/fluid/operators/truncated_gaussian_random_op.h
+++ b/paddle/fluid/operators/truncated_gaussian_random_op.h
@@ -1,8 +1,11 @@
 /* Copyright (c) 2020 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.
@@ -137,9 +140,19 @@ T Erfinv(T x) {
 template <typename T>
 struct TruncatedNormal {
   T mean, std;
-  TruncatedNormal(T mean, T std) : mean(mean), std(std) {}
+  T a_normal_cdf;
+  T b_normal_cdf;
+  TruncatedNormal(T mean, T std) : mean(mean), std(std) {
+    auto normal_cdf = [](T x) {
+      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
+    };
+    a_normal_cdf = normal_cdf(-2.0);
+    b_normal_cdf = normal_cdf(2.0);
+  }
+
   T operator()(T value) const {
-    return std::sqrt(2.0) * Erfinv(value) * std + mean;
+    auto p = a_normal_cdf + (b_normal_cdf - a_normal_cdf) * value;
+    return std::sqrt(2.0) * Erfinv(2 * p - 1) * std + mean;
   }
 };
 
diff --git a/paddle/fluid/operators/truncated_gaussian_random_op_npu.cc b/paddle/fluid/operators/truncated_gaussian_random_op_npu.cc
index 4ed0dd22ec086923bbe47af192cab8d001ae734f..261d9cee2d5cd25c510aacb280b9623f985eb1f7 100644
--- a/paddle/fluid/operators/truncated_gaussian_random_op_npu.cc
+++ b/paddle/fluid/operators/truncated_gaussian_random_op_npu.cc
@@ -84,13 +84,8 @@ class NPUTruncatedGaussianRandomKernel : public framework::OpKernel<T> {
     Tensor cpu_tensor(tensor->dtype());
     cpu_tensor.Resize(tensor->dims());
     T* cpu_data = cpu_tensor.mutable_data<T>(platform::CPUPlace());
-    auto normal_cdf = [](float x) {
-      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-    };
-    float a_normal_cdf = normal_cdf((-2.0 - mean) / std);
-    float b_normal_cdf = normal_cdf((2.0 - mean) / std);
-    std::uniform_real_distribution<float> dist(2.0 * a_normal_cdf - 1.0,
-                                               2.0 * b_normal_cdf - 1.0);
+    std::uniform_real_distribution<T> dist(std::numeric_limits<float>::min(),
+                                           1.0);
     TruncatedNormal<T> truncated_normal(mean, std);
     int64_t size = tensor->numel();
 
diff --git a/paddle/fluid/operators/truncated_gaussian_random_op_xpu.cc b/paddle/fluid/operators/truncated_gaussian_random_op_xpu.cc
index 984d9f397cc655b4cfd7e0bc211db1665252272f..803b61fbe813f85f48b71d1de7fc41eb26e4b8da 100644
--- a/paddle/fluid/operators/truncated_gaussian_random_op_xpu.cc
+++ b/paddle/fluid/operators/truncated_gaussian_random_op_xpu.cc
@@ -32,13 +32,8 @@ class XPUTruncatedGaussianRandomKernel : public framework::OpKernel<T> {
     auto* tensor = context.Output<framework::Tensor>("Out");
     T* data = tensor->mutable_data<T>(context.GetPlace());
 
-    auto normal_cdf = [](float x) {
-      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-    };
-    float a_normal_cdf = normal_cdf((-2.0 - mean) / std);
-    float b_normal_cdf = normal_cdf((2.0 - mean) / std);
-    std::uniform_real_distribution<float> dist(2.0 * a_normal_cdf - 1.0,
-                                               2.0 * b_normal_cdf - 1.0);
+    std::uniform_real_distribution<T> dist(std::numeric_limits<float>::min(),
+                                           1.0);
     TruncatedNormal<T> truncated_normal(mean, std);
     int64_t size = tensor->numel();
 
diff --git a/paddle/phi/kernels/cpu/truncated_gaussian_random_kernel.cc b/paddle/phi/kernels/cpu/truncated_gaussian_random_kernel.cc
index ab3d3c2376b8b05b4909f2c44df260299c2fe460..4247e597acef4aac14f93066a3ea6232734e0c8c 100644
--- a/paddle/phi/kernels/cpu/truncated_gaussian_random_kernel.cc
+++ b/paddle/phi/kernels/cpu/truncated_gaussian_random_kernel.cc
@@ -37,13 +37,8 @@ void TruncatedGaussianRandomKernel(const Context& dev_ctx,
 
   T* data = dev_ctx.template Alloc<T>(tensor);
 
-  auto normal_cdf = [](float x) {
-    return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-  };
-  float a_normal_cdf = normal_cdf((-2.0 - mean) / std);
-  float b_normal_cdf = normal_cdf((2.0 - mean) / std);
-  std::uniform_real_distribution<float> dist(2.0 * a_normal_cdf - 1.0,
-                                             2.0 * b_normal_cdf - 1.0);
+  std::uniform_real_distribution<T> dist(std::numeric_limits<float>::min(),
+                                         1.0);
   TruncatedNormal<T> truncated_normal(mean, std);
   int64_t size = tensor->numel();
 
diff --git a/paddle/phi/kernels/gpu/truncated_gaussian_random_kernel.cu b/paddle/phi/kernels/gpu/truncated_gaussian_random_kernel.cu
index bb04e7ee8515bb6320860e4fd20366995d26c991..f27b32ca7b8319440b62f0d03d21129133c8470c 100644
--- a/paddle/phi/kernels/gpu/truncated_gaussian_random_kernel.cu
+++ b/paddle/phi/kernels/gpu/truncated_gaussian_random_kernel.cu
@@ -33,27 +33,23 @@ struct GPUTruncatedNormal {
   T mean, std;
   T a_normal_cdf;
   T b_normal_cdf;
-
   unsigned int seed;
   T numeric_min;
 
   __host__ __device__ GPUTruncatedNormal(T mean, T std, T numeric_min, int seed)
       : mean(mean), std(std), seed(seed), numeric_min(numeric_min) {
-    auto normal_cdf = [](float x) {
-      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-    };
-    a_normal_cdf = normal_cdf((-2.0 - mean) / std);
-    b_normal_cdf = normal_cdf((2.0 - mean) / std);
+    a_normal_cdf = (1.0 + erff(-2.0 / sqrtf(2.0))) / 2.0;
+    b_normal_cdf = (1.0 + erff(2.0 / sqrtf(2.0))) / 2.0;
   }
 
   __host__ __device__ T operator()(const unsigned int n) const {
     thrust::minstd_rand rng;
     rng.seed(seed);
-    thrust::uniform_real_distribution<T> dist(2.0 * a_normal_cdf - 1.0,
-                                              2.0 * b_normal_cdf - 1.0);
+    thrust::uniform_real_distribution<T> dist(numeric_min, 1);
     rng.discard(n);
     T value = dist(rng);
-    return std::sqrt(2.0) * erfinvf(value) * std + mean;
+    auto p = a_normal_cdf + (b_normal_cdf - a_normal_cdf) * value;
+    return std::sqrt(2.0) * erfinvf(2 * p - 1) * std + mean;
   }
 };
 
@@ -73,21 +69,18 @@ struct TruncatedNormalOffset {
         seed(seed),
         numeric_min(numeric_min),
         offset_(offset) {
-    auto normal_cdf = [](float x) {
-      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
-    };
-    a_normal_cdf = normal_cdf((-2.0 - mean) / std);
-    b_normal_cdf = normal_cdf((2.0 - mean) / std);
+    a_normal_cdf = (1.0 + erff(-2.0 / sqrtf(2.0))) / 2.0;
+    b_normal_cdf = (1.0 + erff(2.0 / sqrtf(2.0))) / 2.0;
   }
 
   __host__ __device__ T operator()(const unsigned int n) const {
     thrust::minstd_rand rng;
     rng.seed(seed);
-    thrust::uniform_real_distribution<T> dist(2.0 * a_normal_cdf - 1.0,
-                                              2.0 * b_normal_cdf - 1.0);
+    thrust::uniform_real_distribution<T> dist(numeric_min, 1);
     rng.discard(n + offset_);
     T value = dist(rng);
-    return std::sqrt(2.0) * erfinvf(value) * std + mean;
+    auto p = a_normal_cdf + (b_normal_cdf - a_normal_cdf) * value;
+    return std::sqrt(2.0) * erfinvf(2 * p - 1) * std + mean;
   }
 };
 
diff --git a/paddle/phi/kernels/truncated_gaussian_random_kernel.h b/paddle/phi/kernels/truncated_gaussian_random_kernel.h
index c4c13578a989961839600d8ee403e478c76d1345..f8547ced41934a9810dc6874c090ab5aefd43497 100644
--- a/paddle/phi/kernels/truncated_gaussian_random_kernel.h
+++ b/paddle/phi/kernels/truncated_gaussian_random_kernel.h
@@ -141,9 +141,19 @@ T Erfinv(T x) {
 template <typename T>
 struct TruncatedNormal {
   T mean, std;
-  TruncatedNormal(T mean, T std) : mean(mean), std(std) {}
+  T a_normal_cdf;
+  T b_normal_cdf;
+  TruncatedNormal(T mean, T std) : mean(mean), std(std) {
+    auto normal_cdf = [](T x) {
+      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
+    };
+    a_normal_cdf = normal_cdf(-2.0);
+    b_normal_cdf = normal_cdf(2.0);
+  }
+
   T operator()(T value) const {
-    return std::sqrt(2.0) * Erfinv(value) * std + mean;
+    auto p = a_normal_cdf + (b_normal_cdf - a_normal_cdf) * value;
+    return std::sqrt(2.0) * Erfinv(2 * p - 1) * std + mean;
   }
 };