diff --git a/news/4299.feature b/news/4299.feature
new file mode 100644
index 00000000000..0f9f3c618b4
--- /dev/null
+++ b/news/4299.feature
@@ -0,0 +1 @@
+Support build-numbers in wheel versions and support sorting with build-numbers.
diff --git a/pip/index.py b/pip/index.py
index 5808b921a88..46f97e8e39a 100644
--- a/pip/index.py
+++ b/pip/index.py
@@ -278,6 +278,7 @@ def _candidate_sort_key(self, candidate):
               with the same version, would have to be considered equal
         """
         support_num = len(self.valid_tags)
+        build_tag = tuple()
         if candidate.location.is_wheel:
             # can raise InvalidWheelFilename
             wheel = Wheel(candidate.location.filename)
@@ -287,9 +288,13 @@ def _candidate_sort_key(self, candidate):
                     "can't be sorted." % wheel.filename
                 )
             pri = -(wheel.support_index_min(self.valid_tags))
+            if wheel.build_tag is not None:
+                match = re.match('^(\d+)(.*)$', wheel.build_tag)
+                build_tag_groups = match.groups()
+                build_tag = (int(build_tag_groups[0]), build_tag_groups[1])
         else:  # sdist
             pri = -(support_num)
-        return (candidate.version, pri)
+        return (candidate.version, build_tag, pri)
 
     def _validate_secure_origin(self, logger, location):
         # Determine if this url used a secure transport mechanism
diff --git a/pip/wheel.py b/pip/wheel.py
index 31cceed19ef..3727522cd43 100644
--- a/pip/wheel.py
+++ b/pip/wheel.py
@@ -482,7 +482,7 @@ class Wheel(object):
 
     wheel_file_re = re.compile(
         r"""^(?P<namever>(?P<name>.+?)-(?P<ver>.*?))
-        ((-(?P<build>\d.*?))?-(?P<pyver>.+?)-(?P<abi>.+?)-(?P<plat>.+?)
+        ((-(?P<build>\d[^-]*?))?-(?P<pyver>.+?)-(?P<abi>.+?)-(?P<plat>.+?)
         \.whl|\.dist-info)$""",
         re.VERBOSE
     )
@@ -501,6 +501,7 @@ def __init__(self, filename):
         # we'll assume "_" means "-" due to wheel naming scheme
         # (https://github.com/pypa/pip/issues/1150)
         self.version = wheel_info.group('ver').replace('_', '-')
+        self.build_tag = wheel_info.group('build')
         self.pyversions = wheel_info.group('pyver').split('.')
         self.abis = wheel_info.group('abi').split('.')
         self.plats = wheel_info.group('plat').split('.')
diff --git a/tests/data/packages/simplewheel-2.0-1-py2.py3-none-any.whl b/tests/data/packages/simplewheel-2.0-1-py2.py3-none-any.whl
new file mode 100644
index 00000000000..acf0c56cfd9
Binary files /dev/null and b/tests/data/packages/simplewheel-2.0-1-py2.py3-none-any.whl differ
diff --git a/tests/unit/test_finder.py b/tests/unit/test_finder.py
index 638d1f9cdd1..7cfb6d48019 100644
--- a/tests/unit/test_finder.py
+++ b/tests/unit/test_finder.py
@@ -251,6 +251,31 @@ def test_link_sorting(self):
 
         assert links == results == results2, results2
 
+    def test_link_sorting_wheels_with_build_tags(self):
+        """Verify build tags affect sorting."""
+        links = [
+            InstallationCandidate(
+                "simplewheel",
+                "2.0",
+                Link("simplewheel-2.0-1-py2.py3-none-any.whl"),
+            ),
+            InstallationCandidate(
+                "simplewheel",
+                "2.0",
+                Link("simplewheel-2.0-py2.py3-none-any.whl"),
+            ),
+            InstallationCandidate(
+                "simplewheel",
+                "1.0",
+                Link("simplewheel-1.0-py2.py3-none-any.whl"),
+            ),
+        ]
+        finder = PackageFinder([], [], session=PipSession())
+        results = sorted(links, key=finder._candidate_sort_key, reverse=True)
+        results2 = sorted(reversed(links), key=finder._candidate_sort_key,
+                          reverse=True)
+        assert links == results == results2, results2
+
 
 def test_finder_priority_file_over_page(data):
     """Test PackageFinder prefers file links over equivalent page links"""