diff --git a/Lib/modulefinder.py b/Lib/modulefinder.py
--- a/Lib/modulefinder.py
+++ b/Lib/modulefinder.py
@@ -1,12 +1,13 @@
 """Find modules used by a script, using introspection."""
 
 import dis
 import imp
+import importlib.machinery
 import marshal
 import os
 import sys
 import types
 import struct
 
 # XXX Clean up once str8's cstor matches bytes.
 LOAD_CONST = bytes([dis.opname.index('LOAD_CONST')])
diff --git a/Lib/test/test_modulefinder.py b/Lib/test/test_modulefinder.py
--- a/Lib/test/test_modulefinder.py
+++ b/Lib/test/test_modulefinder.py
@@ -191,16 +191,28 @@ relative_import_test_3 = [
     """\
 a/__init__.py
                                 def foo(): pass
 a/module.py
                                 from . import foo
                                 from . import bar
 """]
 
+relative_import_test_4 = [
+    "a.module",
+    ["a", "a.module"],
+    [],
+    [],
+    """\
+a/__init__.py
+                                def foo(): pass
+a/module.py
+                                from . import *
+"""]
+
 
 def open_file(path):
     dirname = os.path.dirname(path)
     try:
         os.makedirs(dirname)
     except OSError as e:
         if e.errno != errno.EEXIST:
             raise
@@ -268,14 +280,17 @@ class ModuleFinderTest(unittest.TestCase
         self._do_test(relative_import_test)
 
     def test_relative_imports_2(self):
         self._do_test(relative_import_test_2)
 
     def test_relative_imports_3(self):
         self._do_test(relative_import_test_3)
 
+    def test_relative_imports_4(self):
+        self._do_test(relative_import_test_4)
+
 
 def test_main():
     support.run_unittest(ModuleFinderTest)
 
 if __name__ == "__main__":
     unittest.main()