diff --git a/colossalai/amp/naive_amp/grad_scaler/__init__.py b/colossalai/amp/naive_amp/grad_scaler/__init__.py
new file mode 100644
index 000000000..dc8499d87
--- /dev/null
+++ b/colossalai/amp/naive_amp/grad_scaler/__init__.py
@@ -0,0 +1,5 @@
+from .base_grad_scaler import BaseGradScaler
+from .constant_grad_scaler import ConstantGradScaler
+from .dynamic_grad_scaler import DynamicGradScaler
+
+__all__ = ['BaseGradScaler', 'ConstantGradScaler', 'DynamicGradScaler']
diff --git a/colossalai/amp/naive_amp/grad_scaler/base_grad_scaler.py b/colossalai/amp/naive_amp/grad_scaler/base_grad_scaler.py
new file mode 100644
index 000000000..fb279baf6
--- /dev/null
+++ b/colossalai/amp/naive_amp/grad_scaler/base_grad_scaler.py
@@ -0,0 +1,46 @@
+#!/usr/bin/env python
+# -*- encoding: utf-8 -*-
+
+import torch
+from abc import ABC, abstractmethod
+from colossalai.logging import get_dist_logger
+from torch import Tensor
+from typing import Dict
+
+__all__ = ['BaseGradScaler']
+
+
+class BaseGradScaler(ABC):
+
+    def __init__(self, initial_scale: int, verbose: bool):
+        assert initial_scale > 0
+        self._scale = torch.cuda.FloatTensor([initial_scale])
+        self._verbose = verbose
+
+        if self._verbose:
+            self._logger = get_dist_logger()
+
+    @property
+    def scale(self) -> Tensor:
+        return self._scale
+
+    @property
+    def inv_scale(self) -> Tensor:
+        return self._scale.double().reciprocal().float()
+
+    @abstractmethod
+    def state_dict(self) -> Dict:
+        state_dict = dict()
+        state_dict['scale'] = self.scale
+
+    @abstractmethod
+    def load_state_dict(self, state_dict: Dict) -> None:
+        self._scale = state_dict['scale']
+
+    @abstractmethod
+    def update(self, overflow: bool) -> None:
+        pass
+
+    def log(self, message, *args, **kwargs):
+        if self._verbose:
+            self._logger.info(message, *args, **kwargs)
diff --git a/colossalai/amp/naive_amp/grad_scaler/constant_grad_scaler.py b/colossalai/amp/naive_amp/grad_scaler/constant_grad_scaler.py
new file mode 100644
index 000000000..5f79462b3
--- /dev/null
+++ b/colossalai/amp/naive_amp/grad_scaler/constant_grad_scaler.py
@@ -0,0 +1,16 @@
+#!/usr/bin/env python
+# -*- encoding: utf-8 -*-
+from .base_grad_scaler import BaseGradScaler
+
+__all__ = ['ConstantGradScaler']
+
+
+class ConstantGradScaler(BaseGradScaler):
+
+    def __init__(self, initial_scale: int, verbose: bool):
+        super().__init__(initial_scale, verbose)
+        self.log(f"Constant Gradient Scaler is initialized with scale {self.scale}", ranks=[0])
+
+    def update(self, overflow: bool) -> None:
+        # do nothing to maintain the current scale value
+        pass
diff --git a/colossalai/amp/naive_amp/grad_scaler/dynamic_grad_scaler.py b/colossalai/amp/naive_amp/grad_scaler/dynamic_grad_scaler.py
new file mode 100644
index 000000000..79fd0f3a3
--- /dev/null
+++ b/colossalai/amp/naive_amp/grad_scaler/dynamic_grad_scaler.py
@@ -0,0 +1,68 @@
+#!/usr/bin/env python
+# -*- encoding: utf-8 -*-
+
+import torch
+from .base_grad_scaler import BaseGradScaler
+
+__all__ = ['DynamicGradScaler']
+
+
+class DynamicGradScaler(BaseGradScaler):
+
+    def __init__(self,
+                 initial_scale: int = 2**16,
+                 growth_factor: int = 2,
+                 backoff_factor: float = 0.5,
+                 growth_interval: int = 1000,
+                 min_scale: int = None,
+                 max_scale: int = None,
+                 hysteresis: int = None,
+                 verbose: bool = False):
+        super().__init__(initial_scale, verbose)
+        self._min_scale = min_scale
+        self._max_scale = max_scale
+        self._growth_factor = growth_factor
+        self._backoff_factor = backoff_factor
+        self._growth_interval = growth_interval
+        self._growth_step = 0
+        self._hysteresis = hysteresis
+        self._hysteresis_step = 0
+        self._sanity_checks()
+
+    def _sanity_checks(self) -> None:
+        if self._min_scale:
+            assert self._min_scale > 0, 'The minimum gradient scale cannot be zero or negative'
+        if self._max_scale:
+            assert self._min_scale > 0, 'The maximum gradient scale cannot be zero or negative'
+        assert self._growth_factor > 1, 'The growth factor cannot be equal or smaller than 1'
+        assert self._backoff_factor < 1 and self._backoff_factor > 0, 'The backoff factor must be between 0 and 1'
+        assert self._hysteresis >= 0, 'The hysteresis cannot be negative'
+
+    def update(self, overflow: bool) -> None:
+        if overflow:
+            self._hysteresis_step += 1
+            self._growth_step = 0
+
+            if self._hysteresis_step >= self._hysteresis:
+                self._backoff_scale()
+                self.log(f"Overflow occurs, the loss scale is adjusted to {self.scale.item()}", ranks=[0])
+        else:
+            self._growth_step += 1
+            if self._growth_step == self._growth_interval:
+                self._growth_step = 0
+                self._hysteresis_step = 0
+                self._grow_scale()
+                self.log(
+                    f"No overflow for consecutive {self._growth_interval} steps, "
+                    f"the loss scale is adjusted to {self.scale.item()}",
+                    ranks=[0])
+
+    def _backoff_scale(self) -> None:
+        self._scale = self._scale * self._backoff_factor
+        if self._min_scale:
+            self._scale = torch.max(self._scale, self._min_scale)
+
+    def _grow_scale(self) -> None:
+        self._scale = self._scale * self._growth_factor
+        if self._max_scale:
+            self._scale = torch.min(self._scale, self._max_scale)