diff --git a/dpdata/cli.py b/dpdata/cli.py
index ef6eeab77..2b33f9590 100644
--- a/dpdata/cli.py
+++ b/dpdata/cli.py
@@ -1,5 +1,6 @@
 """Command line interface for dpdata."""
 import argparse
+from typing import Optional
 
 from . import __version__
 from .system import System, LabeledSystem, MultiSystems
@@ -47,11 +48,11 @@ def dpdata_cli():
 def convert(*,
             from_file: str,
             from_format: str = "auto",
-            to_file: str = None,
-            to_format: str = None,
+            to_file: Optional[str] = None,
+            to_format: Optional[str] = None,
             no_labeled: bool = False,
             multi: bool = False,
-            type_map: list = None,
+            type_map: Optional[list] = None,
             **kwargs):
     """Convert files from one format to another one.
     
diff --git a/dpdata/deepmd/hdf5.py b/dpdata/deepmd/hdf5.py
index 8bbd00484..0e807f058 100644
--- a/dpdata/deepmd/hdf5.py
+++ b/dpdata/deepmd/hdf5.py
@@ -1,5 +1,5 @@
 """Utils for deepmd/hdf5 format."""
-from typing import Union
+from typing import Optional, Union
 
 import h5py
 import numpy as np
@@ -11,7 +11,7 @@
 
 def to_system_data(f: Union[h5py.File, h5py.Group],
                    folder: str, 
-                   type_map: list = None,
+                   type_map: Optional[list] = None,
                    labels: bool = True) :
     """Load a HDF5 file.
 
diff --git a/dpdata/gaussian/gjf.py b/dpdata/gaussian/gjf.py
index 588f1ed67..727732b86 100644
--- a/dpdata/gaussian/gjf.py
+++ b/dpdata/gaussian/gjf.py
@@ -3,7 +3,7 @@
 # under LGPL 3.0 license
 """Generate Gaussian input file."""
 
-from typing import List, Tuple, Union
+from typing import Optional, List, Tuple, Union
 import uuid
 import itertools
 import warnings
@@ -107,8 +107,8 @@ def make_gaussian_input(
         multiplicity: Union[str ,int] = "auto",
         charge: int = 0,
         fragment_guesses: bool = False,
-        basis_set: str = None,
-        keywords_high_multiplicity: str = None,
+        basis_set: Optional[str] = None,
+        keywords_high_multiplicity: Optional[str] = None,
         nproc: int = 1,
         ) -> str:
     """Make gaussian input file.
diff --git a/dpdata/plugins/ase.py b/dpdata/plugins/ase.py
index 728df3298..fa2093e40 100644
--- a/dpdata/plugins/ase.py
+++ b/dpdata/plugins/ase.py
@@ -1,4 +1,4 @@
-from typing import TYPE_CHECKING, Type
+from typing import Optional, TYPE_CHECKING, Type
 from dpdata.driver import Driver, Minimizer
 from dpdata.format import Format
 import numpy as np
@@ -93,7 +93,7 @@ def from_labeled_system(self, atoms: "ase.Atoms", **kwargs) -> dict:
             info_dict['virials'] = virials
         return info_dict
 
-    def from_multi_systems(self, file_name: str, begin: int=None, end: int=None, step: int=None, ase_fmt: str=None, **kwargs) -> "ase.Atoms":
+    def from_multi_systems(self, file_name: str, begin: Optional[int] = None, end: Optional[int] = None, step: Optional[int] = None, ase_fmt: Optional[str] = None, **kwargs) -> "ase.Atoms":
         """Convert a ASE supported file to ASE Atoms.
 
         It will finally be converted to MultiSystems.
@@ -228,9 +228,9 @@ class ASEMinimizer(Minimizer):
     """
     def __init__(self,
                  driver: Driver,
-                 optimizer: Type["Optimizer"] = None,
+                 optimizer: Optional[Type["Optimizer"]] = None,
                  fmax: float = 5e-3,
-                 max_steps: int = None,
+                 max_steps: Optional[int] = None,
                  optimizer_kwargs: dict = {}) -> None:
         self.calculator = driver.ase_calculator
         if optimizer is None:
diff --git a/dpdata/plugins/deepmd.py b/dpdata/plugins/deepmd.py
index aa69c44b8..c3b7f4ca5 100644
--- a/dpdata/plugins/deepmd.py
+++ b/dpdata/plugins/deepmd.py
@@ -1,4 +1,4 @@
-from typing import Union, List
+from typing import Optional, Union, List
 
 import dpdata
 import dpdata.deepmd.raw
@@ -108,7 +108,7 @@ def _from_system(self, file_name: Union[str, h5py.Group, h5py.File], type_map: L
 
     def from_system(self,
                     file_name: Union[str, h5py.Group, h5py.File],
-                    type_map: List[str]=None,
+                    type_map: Optional[List[str]] = None,
                     **kwargs) -> dict:
         """Convert HDF5 file to System data.
 
@@ -134,7 +134,7 @@ def from_system(self,
 
     def from_labeled_system(self,
                             file_name: Union[str, h5py.Group, h5py.File],
-                            type_map: List[str]=None,
+                            type_map: Optional[List[str]] = None,
                             **kwargs) -> dict:
         """Convert HDF5 file to LabeledSystem data.