diff --git a/Lib/test/test_urlparse.py b/Lib/test/test_urlparse.py
index 4ae6ed33858ce2..cd9173e4d842c5 100644
--- a/Lib/test/test_urlparse.py
+++ b/Lib/test/test_urlparse.py
@@ -157,6 +157,12 @@ def test_roundtrips(self):
             ('file:///tmp/junk.txt',
              ('file', '', '/tmp/junk.txt', '', '', ''),
              ('file', '', '/tmp/junk.txt', '', '')),
+            ('file:////tmp/junk.txt',
+             ('file', '', '//tmp/junk.txt', '', '', ''),
+             ('file', '', '//tmp/junk.txt', '', '')),
+            ('file://///tmp/junk.txt',
+             ('file', '', '///tmp/junk.txt', '', '', ''),
+             ('file', '', '///tmp/junk.txt', '', '')),
             ('imap://mail.python.org/mbox1',
              ('imap', 'mail.python.org', '/mbox1', '', '', ''),
              ('imap', 'mail.python.org', '/mbox1', '', '')),
diff --git a/Lib/urllib/parse.py b/Lib/urllib/parse.py
index b6608783a89471..9de24548612a98 100644
--- a/Lib/urllib/parse.py
+++ b/Lib/urllib/parse.py
@@ -490,7 +490,7 @@ def urlunsplit(components):
     empty query; the RFC states that these are equivalent)."""
     scheme, netloc, url, query, fragment, _coerce_result = (
                                           _coerce_args(*components))
-    if netloc or (scheme and scheme in uses_netloc and url[:2] != '//'):
+    if netloc or (scheme and scheme in uses_netloc):
         if url and url[:1] != '/': url = '/' + url
         url = '//' + (netloc or '') + url
     if scheme:
diff --git a/Misc/NEWS.d/next/Library/2019-08-27-01-16-50.bpo-34276.4NIAiy.rst b/Misc/NEWS.d/next/Library/2019-08-27-01-16-50.bpo-34276.4NIAiy.rst
new file mode 100644
index 00000000000000..d48bf3659e408d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-08-27-01-16-50.bpo-34276.4NIAiy.rst
@@ -0,0 +1 @@
+Makes sure that file URIs with multiple leading slashes (file:////, etc.) are properly round-tripped by urllib.parse. Patch by Ashwin Ramaswami