diff --git a/CHANGES b/CHANGES
index 0aa82cf49..1ff1fd3e2 100644
--- a/CHANGES
+++ b/CHANGES
@@ -17,6 +17,7 @@ Bugs fixed
 ----------
 
 * #4019: inheritance_diagram AttributeError stoping make process
+* #4539: autodoc emits warnings for partialmethods
 
 Testing
 --------
diff --git a/sphinx/util/inspect.py b/sphinx/util/inspect.py
index 3c3361b99..6fd5c789c 100644
--- a/sphinx/util/inspect.py
+++ b/sphinx/util/inspect.py
@@ -307,9 +307,17 @@ class Signature(object):
             raise TypeError("can't compute signature for built-in type {}".format(subject))
 
         self.subject = subject
+        self.partialmethod_with_noargs = False
 
         if PY3:
-            self.signature = inspect.signature(subject)
+            try:
+                self.signature = inspect.signature(subject)
+            except IndexError:
+                if hasattr(subject, '_partialmethod'):  # partialmethod with no argument
+                    self.signature = None
+                    self.partialmethod_with_noargs = True
+                else:
+                    raise
         else:
             self.argspec = getargspec(subject)
 
@@ -339,7 +347,10 @@ class Signature(object):
     def parameters(self):
         # type: () -> Dict
         if PY3:
-            return self.signature.parameters
+            if self.partialmethod_with_noargs:
+                return {}
+            else:
+                return self.signature.parameters
         else:
             params = OrderedDict()  # type: Dict
             positionals = len(self.argspec.args) - len(self.argspec.defaults)
@@ -360,7 +371,7 @@ class Signature(object):
     @property
     def return_annotation(self):
         # type: () -> Any
-        if PY3:
+        if PY3 and self.signature:
             return self.signature.return_annotation
         else:
             return None
diff --git a/tests/roots/test-ext-autodoc/target/partialmethod.py b/tests/roots/test-ext-autodoc/target/partialmethod.py
new file mode 100644
index 000000000..01cf4e798
--- /dev/null
+++ b/tests/roots/test-ext-autodoc/target/partialmethod.py
@@ -0,0 +1,18 @@
+# for py34 or above
+from functools import partialmethod
+
+
+class Cell(object):
+    """An example for partialmethod.
+
+    refs: https://docs.python.jp/3/library/functools.html#functools.partialmethod
+    """
+
+    def set_state(self, state):
+        """Update state of cell to *state*."""
+
+    #: Make a cell alive.
+    set_alive = partialmethod(set_state, True)
+
+    set_dead = partialmethod(set_state, False)
+    """Make a cell dead."""
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index 55c4b8847..7de5a2910 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -907,3 +907,50 @@ def test_generate():
     options.members = ['decoratedFunction']
     assert_result_contains('.. py:function:: decoratedFunction()',
                            'module', 'autodoc_missing_imports')
+
+
+@pytest.mark.skipif(sys.version_info < (3, 4),
+                    reason='functools.partialmethod is available on py34 or above')
+@pytest.mark.usefixtures('setup_test')
+def test_partialmethod():
+    def call_autodoc(objtype, name):
+        inst = app.registry.documenters[objtype](directive, name)
+        inst.generate()
+        result = list(directive.result)
+        del directive.result[:]
+        return result
+
+    options.inherited_members = True
+    options.undoc_members = True
+    expected = [
+        '',
+        '.. py:class:: Cell',
+        '   :module: target.partialmethod',
+        '',
+        '   An example for partialmethod.',
+        '   ',
+        '   refs: https://docs.python.jp/3/library/functools.html#functools.partialmethod',
+        '   ',
+        '   ',
+        '   .. py:method:: Cell.set_alive() -> None',
+        '      :module: target.partialmethod',
+        '   ',
+        '      Make a cell alive.',
+        '      ',
+        '   ',
+        '   .. py:method:: Cell.set_dead() -> None',
+        '      :module: target.partialmethod',
+        '   ',
+        '      Make a cell dead.',
+        '      ',
+        '   ',
+        '   .. py:method:: Cell.set_state(state)',
+        '      :module: target.partialmethod',
+        '   ',
+        '      Update state of cell to *state*.',
+        '      ',
+    ]
+    if sys.version_info < (3, 5):
+        expected = '\n'.join(expected).replace(' -> None', '').split('\n')
+
+    assert call_autodoc('class', 'target.partialmethod.Cell') == expected
diff --git a/tests/test_util_inspect.py b/tests/test_util_inspect.py
index b5d50ed71..3e4c82d5b 100644
--- a/tests/test_util_inspect.py
+++ b/tests/test_util_inspect.py
@@ -200,6 +200,33 @@ def test_Signature_methods():
         assert sig == '(arg1, **kwargs)'
 
 
+@pytest.mark.skipif(sys.version_info < (3, 4),
+                    reason='functools.partialmethod is available on py34 or above')
+def test_Signature_partialmethod():
+    from functools import partialmethod
+
+    class Foo(object):
+        def meth1(self, arg1, arg2, arg3=None, arg4=None):
+            pass
+
+        def meth2(self, arg1, arg2):
+            pass
+
+        foo = partialmethod(meth1, 1, 2)
+        bar = partialmethod(meth1, 1, arg3=3)
+        baz = partialmethod(meth2, 1, 2)
+
+    subject = Foo()
+    sig = inspect.Signature(subject.foo).format_args()
+    assert sig == '(arg3=None, arg4=None)'
+
+    sig = inspect.Signature(subject.bar).format_args()
+    assert sig == '(arg2, *, arg3=3, arg4=None)'
+
+    sig = inspect.Signature(subject.baz).format_args()
+    assert sig == '()'
+
+
 @pytest.mark.skipif(sys.version_info < (3, 5),
                     reason='type annotation test is available on py35 or above')
 def test_Signature_annotations():