diff --git a/Lib/test/test_modulefinder.py b/Lib/test/test_modulefinder.py
index ca1058b8d4087c..6aee48044264e3 100644
--- a/Lib/test/test_modulefinder.py
+++ b/Lib/test/test_modulefinder.py
@@ -399,6 +399,12 @@ def test_replace_paths(self):
         expected = "co_filename %r changed to %r" % (old_path, new_path)
         self.assertIn(expected, output)
 
+    def test_encoding(self):
+        os.makedirs(TEST_DIR, exist_ok=True)
+        with open(os.path.join(TEST_DIR,'a.py'), 'w', encoding='cp1252') as f:
+            f.write('# -*- coding: cp1252 -*-\nx = "€"\n')
+        self._do_test(["a", ["a"], [], [], ""])
+
     def test_extended_opargs(self):
         extended_opargs_test = [
             "a",
diff --git a/Misc/NEWS.d/next/Library/2020-01-06-22-39-23.bpo-39206.zKSTwb.rst b/Misc/NEWS.d/next/Library/2020-01-06-22-39-23.bpo-39206.zKSTwb.rst
new file mode 100644
index 00000000000000..d3e7801e4e6a20
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-01-06-22-39-23.bpo-39206.zKSTwb.rst
@@ -0,0 +1 @@
+Fix :mod:`modulefinder` to handle :pep:`263` encoding markers - by Luciana Marques