diff --git a/Doc/library/urllib.request.rst b/Doc/library/urllib.request.rst
index a5f1b9b292a85a..b7c0c7d5099806 100644
--- a/Doc/library/urllib.request.rst
+++ b/Doc/library/urllib.request.rst
@@ -199,9 +199,9 @@ The :mod:`urllib.request` module defines the following functions:
 
    .. versionchanged:: next
       This function calls :func:`socket.gethostbyname` if the URL authority
-      isn't empty or ``localhost``. If the authority resolves to a local IP
-      address then it is discarded; otherwise, on Windows a UNC path is
-      returned (as before), and on other platforms a
+      isn't empty, ``localhost``, or the machine hostname. If the authority
+      resolves to a local IP address then it is discarded; otherwise, on
+      Windows a UNC path is returned (as before), and on other platforms a
       :exc:`~urllib.error.URLError` is raised.
 
    .. versionchanged:: next
diff --git a/Lib/urllib/request.py b/Lib/urllib/request.py
index 2c9c7b6ca5394d..9a6b29a90a2968 100644
--- a/Lib/urllib/request.py
+++ b/Lib/urllib/request.py
@@ -1483,8 +1483,17 @@ def open_local_file(self, req):
     file_open = open_local_file
 
 def _is_local_authority(authority):
+    # Compare hostnames
     if not authority or authority == 'localhost':
         return True
+    try:
+        hostname = socket.gethostname()
+    except (socket.gaierror, AttributeError):
+        pass
+    else:
+        if authority == hostname:
+            return True
+    # Compare IP addresses
     try:
         address = socket.gethostbyname(authority)
     except (socket.gaierror, AttributeError):