diff --git a/Lib/pathlib.py b/Lib/pathlib.py
index b999ab24fb9..8d08e8b4139 100644
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -755,6 +755,12 @@ class PurePath(object):
     def with_suffix(self, suffix):
         """Return a new path with the file suffix changed (or added, if none)."""
         # XXX if suffix is None, should the current suffix be removed?
+        drv, root, parts = self._flavour.parse_parts((suffix,))
+        if drv or root or len(parts) != 1:
+            raise ValueError("Invalid suffix %r" % (suffix))
+        suffix = parts[0]
+        if not suffix.startswith('.'):
+            raise ValueError("Invalid suffix %r" % (suffix))
         name = self.name
         if not name:
             raise ValueError("%r has an empty name" % (self,))
diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
index b6deedb46af..a54eef5e9cd 100755
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -528,9 +528,16 @@ class _BasePurePathTest(object):
         self.assertEqual(P('/a/b').with_suffix('.gz'), P('/a/b.gz'))
         self.assertEqual(P('a/b.py').with_suffix('.gz'), P('a/b.gz'))
         self.assertEqual(P('/a/b.py').with_suffix('.gz'), P('/a/b.gz'))
+        # Path doesn't have a "filename" component
         self.assertRaises(ValueError, P('').with_suffix, '.gz')
         self.assertRaises(ValueError, P('.').with_suffix, '.gz')
         self.assertRaises(ValueError, P('/').with_suffix, '.gz')
+        # Invalid suffix
+        self.assertRaises(ValueError, P('a/b').with_suffix, 'gz')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '/')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '/.gz')
+        self.assertRaises(ValueError, P('a/b').with_suffix, 'c/d')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '.c/.d')
 
     def test_relative_to_common(self):
         P = self.cls
@@ -920,10 +927,23 @@ class PureWindowsPathTest(_BasePurePathTest, unittest.TestCase):
         self.assertEqual(P('c:/a/b').with_suffix('.gz'), P('c:/a/b.gz'))
         self.assertEqual(P('c:a/b.py').with_suffix('.gz'), P('c:a/b.gz'))
         self.assertEqual(P('c:/a/b.py').with_suffix('.gz'), P('c:/a/b.gz'))
+        # Path doesn't have a "filename" component
         self.assertRaises(ValueError, P('').with_suffix, '.gz')
         self.assertRaises(ValueError, P('.').with_suffix, '.gz')
         self.assertRaises(ValueError, P('/').with_suffix, '.gz')
         self.assertRaises(ValueError, P('//My/Share').with_suffix, '.gz')
+        # Invalid suffix
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, 'gz')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '/')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '\\')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, 'c:')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '/.gz')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '\\.gz')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, 'c:.gz')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, 'c/d')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, 'c\\d')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '.c/d')
+        self.assertRaises(ValueError, P('c:a/b').with_suffix, '.c\\d')
 
     def test_relative_to(self):
         P = self.cls
diff --git a/Misc/NEWS b/Misc/NEWS
index 6cce3be89c0..89cd9d1ffa8 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -44,6 +44,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #20111: pathlib.Path.with_suffix() now sanity checks the given suffix.
+
 - Fix breakage in TestSuite.countTestCases() introduced by issue #11798.
 
 - Issue #20108: Avoid parameter name clash in inspect.getcallargs().