diff --git a/CHANGES b/CHANGES
index 65a69f6b8..3263f9fb5 100644
--- a/CHANGES
+++ b/CHANGES
@@ -58,7 +58,7 @@ Features added
 * #6830: autodoc: consider a member private if docstring contains
   ``:meta private:`` in info-field-list
 * #7165: autodoc: Support Annotated type (PEP-593)
-* #2815: autodoc: Support singledispatch functions
+* #2815: autodoc: Support singledispatch functions and methods
 * #6558: glossary: emit a warning for duplicated glossary entry
 * #3106: domain: Register hyperlink target for index page automatically
 * #6558: std domain: emit a warning for duplicated generic objects
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index f6d581cfc..97995a410 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1457,6 +1457,66 @@ class MethodDocumenter(DocstringSignatureMixin, ClassLevelDocumenter):  # type:
         pass
 
 
+class SingledispatchMethodDocumenter(MethodDocumenter):
+    """
+    Specialized Documenter subclass for singledispatch'ed methods.
+    """
+    objtype = 'singledispatch_method'
+    directivetype = 'method'
+    member_order = 50
+
+    # before MethodDocumenter
+    priority = MethodDocumenter.priority + 1
+
+    @classmethod
+    def can_document_member(cls, member: Any, membername: str, isattr: bool, parent: Any
+                            ) -> bool:
+        if super().can_document_member(member, membername, isattr, parent) and parent.object:
+            meth = parent.object.__dict__.get(membername)
+            return inspect.is_singledispatch_method(meth)
+        else:
+            return False
+
+    def add_directive_header(self, sig: str) -> None:
+        sourcename = self.get_sourcename()
+
+        # intercept generated directive headers
+        # TODO: It is very hacky to use mock to intercept header generation
+        with patch.object(self, 'add_line') as add_line:
+            super().add_directive_header(sig)
+
+        # output first line of header
+        self.add_line(*add_line.call_args_list[0][0])
+
+        # inserts signature of singledispatch'ed functions
+        meth = self.parent.__dict__.get(self.objpath[-1])
+        for typ, func in meth.dispatcher.registry.items():
+            if typ is object:
+                pass  # default implementation. skipped.
+            else:
+                self.annotate_to_first_argument(func, typ)
+
+                documenter = MethodDocumenter(self.directive, '')
+                documenter.object = func
+                self.add_line('   %s%s' % (self.format_name(),
+                                           documenter.format_signature()),
+                              sourcename)
+
+        # output remains of directive header
+        for call in add_line.call_args_list[1:]:
+            self.add_line(*call[0])
+
+    def annotate_to_first_argument(self, func: Callable, typ: Type) -> None:
+        """Annotate type hint to the first argument of function if needed."""
+        sig = inspect.signature(func, bound_method=True)
+        if len(sig.parameters) == 0:
+            return
+
+        name = list(sig.parameters)[0]
+        if name not in func.__annotations__:
+            func.__annotations__[name] = typ
+
+
 class AttributeDocumenter(DocstringStripSignatureMixin, ClassLevelDocumenter):  # type: ignore
     """
     Specialized Documenter subclass for attributes.
@@ -1672,6 +1732,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_autodocumenter(SingledispatchFunctionDocumenter)
     app.add_autodocumenter(DecoratorDocumenter)
     app.add_autodocumenter(MethodDocumenter)
+    app.add_autodocumenter(SingledispatchMethodDocumenter)
     app.add_autodocumenter(AttributeDocumenter)
     app.add_autodocumenter(PropertyDocumenter)
     app.add_autodocumenter(InstanceAttributeDocumenter)
diff --git a/sphinx/util/inspect.py b/sphinx/util/inspect.py
index 58f922cae..d22df7656 100644
--- a/sphinx/util/inspect.py
+++ b/sphinx/util/inspect.py
@@ -235,6 +235,15 @@ def is_singledispatch_function(obj: Any) -> bool:
         return False
 
 
+def is_singledispatch_method(obj: Any) -> bool:
+    """Check if the object is singledispatch method."""
+    try:
+        from functools import singledispatchmethod  # type: ignore
+        return isinstance(obj, singledispatchmethod)
+    except ImportError:  # py35-37
+        return False
+
+
 def isfunction(obj: Any) -> bool:
     """Check if the object is function."""
     return inspect.isfunction(unwrap(obj))
diff --git a/tests/roots/test-ext-autodoc/target/singledispatchmethod.py b/tests/roots/test-ext-autodoc/target/singledispatchmethod.py
new file mode 100644
index 000000000..b5ccbb2f0
--- /dev/null
+++ b/tests/roots/test-ext-autodoc/target/singledispatchmethod.py
@@ -0,0 +1,20 @@
+from functools import singledispatchmethod
+
+
+class Foo:
+    """docstring"""
+
+    @singledispatchmethod
+    def meth(self, arg, kwarg=None):
+        """A method for general use."""
+        pass
+
+    @meth.register(int)
+    def _meth_int(self, arg, kwarg=None):
+        """A method for int."""
+        pass
+
+    @meth.register(str)
+    def _meth_str(self, arg, kwarg=None):
+        """A method for str."""
+        pass
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index dcbdc6d3a..0510fff86 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -1582,3 +1582,30 @@ def test_singledispatch():
         '   A function for general use.',
         '   '
     ]
+
+
+@pytest.mark.skipif(sys.version_info < (3, 8),
+                    reason='singledispatchmethod is available since python3.8')
+@pytest.mark.usefixtures('setup_test')
+def test_singledispatchmethod():
+    options = {"members": None}
+    actual = do_autodoc(app, 'module', 'target.singledispatchmethod', options)
+    assert list(actual) == [
+        '',
+        '.. py:module:: target.singledispatchmethod',
+        '',
+        '',
+        '.. py:class:: Foo',
+        '   :module: target.singledispatchmethod',
+        '',
+        '   docstring',
+        '   ',
+        '   ',
+        '   .. py:method:: Foo.meth(arg, kwarg=None)',
+        '      Foo.meth(arg: int, kwarg=None)',
+        '      Foo.meth(arg: str, kwarg=None)',
+        '      :module: target.singledispatchmethod',
+        '   ',
+        '      A method for general use.',
+        '      '
+    ]