diff --git a/sphinx/ext/napoleon/docstring.py b/sphinx/ext/napoleon/docstring.py
index 7f6f21d32..48daa8ada 100644
--- a/sphinx/ext/napoleon/docstring.py
+++ b/sphinx/ext/napoleon/docstring.py
@@ -904,7 +904,7 @@ def _token_type(token):
 def _convert_numpy_type_spec(_type, translations={}):
     def convert_obj(obj, translations, default_translation):
         # use :class: (the default) only if obj is not a standard singleton (None, True, False)
-        if obj in (None, True, False) and default_translation == ":class:`{}`":
+        if obj in ("None", "True", "False") and default_translation == ":class:`{}`":
             default_translation = ":obj:`{}`"
 
         return translations.get(obj, default_translation.format(obj))
diff --git a/tests/test_ext_napoleon_docstring.py b/tests/test_ext_napoleon_docstring.py
index 7aa7b2ea2..18eddb72a 100644
--- a/tests/test_ext_napoleon_docstring.py
+++ b/tests/test_ext_napoleon_docstring.py
@@ -2126,8 +2126,8 @@ definition_after_normal_text : int
 
         converted_types = (
             "",
-            ":obj:`str`",
-            ":obj:`int` or :obj:`float` or :obj:`None`",
+            ":class:`str`",
+            ":class:`int` or :class:`float` or :obj:`None`",
             '``{"F", "C", "N"}``',
             "``{'F', 'C', 'N'}``",
         )
@@ -2171,11 +2171,11 @@ definition_after_normal_text : int
             :param param1: the data to work on
             :type param1: DataFrame
             :param param2: a parameter with different types
-            :type param2: :obj:`int` or :obj:`float` or :obj:`None`
+            :type param2: :class:`int` or :class:`float` or :obj:`None`
             :param param3: a optional mapping
             :type param3: :term:`dict-like <mapping>`, *optional*
             :param param4: a optional parameter with different types
-            :type param4: :obj:`int` or :obj:`float` or :obj:`None`, *optional*
+            :type param4: :class:`int` or :class:`float` or :obj:`None`, *optional*
             :param param5: a optional parameter with fixed values
             :type param5: ``{"F", "C", "N"}``, *optional*
         """)