diff --git a/gunicorn/util.py b/gunicorn/util.py
index 456267a1..8aa441d0 100644
--- a/gunicorn/util.py
+++ b/gunicorn/util.py
@@ -21,6 +21,7 @@ import inspect
 import errno
 import warnings
 import logging
+import re
 
 from gunicorn import _compat
 from gunicorn.errors import AppImportError
@@ -232,11 +233,8 @@ def is_ipv6(addr):
 
 
 def parse_address(netloc, default_port=8000):
-    if netloc.startswith("unix://"):
-        return netloc.split("unix://")[1]
-
-    if netloc.startswith("unix:"):
-        return netloc.split("unix:")[1]
+    if re.match(r'unix:(//)?', netloc):
+        return re.split(r'unix:(//)?', netloc)[-1]
 
     if netloc.startswith("tcp://"):
         netloc = netloc.split("tcp://")[1]
diff --git a/tests/test_util.py b/tests/test_util.py
new file mode 100644
index 00000000..fbd0aa21
--- /dev/null
+++ b/tests/test_util.py
@@ -0,0 +1,12 @@
+# -*- coding: utf-8 -
+#
+# This file is part of gunicorn released under the MIT license.
+# See the NOTICE for more information.
+
+from gunicorn import util
+
+
+def test_parse_address():
+    # Test unix socket addresses (PR #1623)
+    assert util.parse_address('unix://var/run/test.sock') == 'var/run/test.sock'
+    assert util.parse_address('unix:/var/run/test.sock') == '/var/run/test.sock'