diff --git a/Lib/test/test_urllib.py b/Lib/test/test_urllib.py
--- a/Lib/test/test_urllib.py
+++ b/Lib/test/test_urllib.py
@@ -268,6 +268,11 @@
         finally:
             self.unfakehttp()
 
+    def test_missing_localfile(self):
+        # Test for #10836
+        with self.assertRaises(urllib.error.URLError):
+            urlopen('file://localhost/a/file/which/doesnot/exists.py')
+
     def test_userpass_inurl(self):
         self.fakehttp(b"HTTP/1.0 200 OK\r\n\r\nHello!")
         try:
diff --git a/Lib/urllib/request.py b/Lib/urllib/request.py
--- a/Lib/urllib/request.py
+++ b/Lib/urllib/request.py
@@ -1658,7 +1658,7 @@
                 return getattr(self, name)(url)
             else:
                 return getattr(self, name)(url, data)
-        except HTTPError:
+        except (HTTPError, URLError):
             raise
         except socket.error as msg:
             raise IOError('socket error', msg).with_traceback(sys.exc_info()[2])
@@ -1885,7 +1885,7 @@
         try:
             stats = os.stat(localname)
         except OSError as e:
-            raise URLError(e.errno, e.strerror, e.filename)
+            raise URLError(e.strerror, e.filename)
         size = stats.st_size
         modified = email.utils.formatdate(stats.st_mtime, usegmt=True)
         mtype = mimetypes.guess_type(url)[0]