diff --git a/Lib/packaging/pypi/simple.py b/Lib/packaging/pypi/simple.py
index 8585193..ee7a113 100644
--- a/Lib/packaging/pypi/simple.py
+++ b/Lib/packaging/pypi/simple.py
@@ -123,8 +123,14 @@
         self.follow_externals = follow_externals
 
         # mirroring attributes.
-        if not index_url.endswith("/"):
-            index_url += "/"
+        parsed = urllib.parse.urlparse(index_url)
+        self.scheme = parsed[0]
+        if self.scheme == 'file':
+            ender = os.path.sep
+        else:
+            ender = '/'
+        if not index_url.endswith(ender):
+            index_url += ender
         # if no mirrors are defined, use the method described in PEP 381.
         if mirrors is None:
             mirrors = get_mirrors(mirrors_url)
@@ -376,7 +382,11 @@
         :param name: the name of the project to find the page
         """
         # Browse and index the content of the given PyPI page.
-        url = self.index_url + name + "/"
+        if self.scheme == 'file':
+            ender = os.path.sep
+        else:
+            ender = '/'
+        url = self.index_url + name + ender
         self._process_url(url, name)
 
     @socket_timeout()
@@ -395,7 +405,7 @@
 
         # add index.html automatically for filesystem paths
         if scheme == 'file':
-            if url.endswith('/'):
+            if url.endswith(os.path.sep):
                 url += "index.html"
 
         # add authorization headers if auth is provided
diff --git a/Lib/packaging/tests/test_pypi_simple.py b/Lib/packaging/tests/test_pypi_simple.py
index 6f0d8d9..d50e3f4 100644
--- a/Lib/packaging/tests/test_pypi_simple.py
+++ b/Lib/packaging/tests/test_pypi_simple.py
@@ -1,5 +1,5 @@
 """Tests for the packaging.pypi.simple module."""
-
+import re
 import os
 import sys
 import http.client
@@ -277,8 +277,16 @@
 
     def test_browse_local_files(self):
         # Test that we can browse local files"""
-        index_path = os.sep.join(["file://" + PYPI_DEFAULT_STATIC_PATH,
-                                  "test_found_links", "simple"])
+        index_url = "file://" + PYPI_DEFAULT_STATIC_PATH
+        if sys.platform == 'win32':
+            # under windows the correct syntax is:
+            #   file:///C|\the\path\here
+            # instead of
+            #   file://C:\the\path\here
+            fix = re.compile(r'^(file://)([A-Za-z])(:)')
+            index_url = fix.sub('\\1/\\2|', index_url)
+
+        index_path = os.sep.join([index_url, "test_found_links", "simple"])
         crawler = Crawler(index_path)
         dists = crawler.get_releases("foobar")
         self.assertEqual(4, len(dists))