diff -r c7f1acdd8be1 Lib/fileinput.py
--- a/Lib/fileinput.py	Mon Feb 01 12:47:15 2016 +0100
+++ b/Lib/fileinput.py	Mon Feb 01 18:56:05 2016 -0500
@@ -412,9 +412,9 @@
         return open(filename, mode)
 
 
-def hook_encoded(encoding):
+def hook_encoded(encoding, errors='strict'):
     def openhook(filename, mode):
-        return open(filename, mode, encoding=encoding)
+        return open(filename, mode, encoding=encoding, errors=errors)
     return openhook
 
 
diff -r c7f1acdd8be1 Lib/test/test_fileinput.py
--- a/Lib/test/test_fileinput.py	Mon Feb 01 12:47:15 2016 +0100
+++ b/Lib/test/test_fileinput.py	Mon Feb 01 18:56:05 2016 -0500
@@ -873,7 +873,8 @@
 
     def test(self):
         encoding = object()
-        result = fileinput.hook_encoded(encoding)
+        errors = object()
+        result = fileinput.hook_encoded(encoding, errors=errors)
 
         fake_open = InvocationRecorder()
         original_open = builtins.open
@@ -891,8 +892,27 @@
         self.assertIs(args[0], filename)
         self.assertIs(args[1], mode)
         self.assertIs(kwargs.pop('encoding'), encoding)
+        self.assertIs(kwargs.pop('errors'), errors)
         self.assertFalse(kwargs)
 
+    def test_errors(self):
+        with open(TESTFN, 'wb') as f:
+            # UTF-7 is a convenient, seldom used encoding
+            f.write(b'\x80abc')
+        self.addCleanup(safe_unlink, TESTFN)
+
+        def check(errors, expected_lines):
+            with FileInput(files=TESTFN, mode='r',
+                           openhook=hook_encoded('utf-8', errors=errors)) as fi:
+                lines = list(fi)
+            self.assertEqual(lines, expected_lines)
+
+        check('ignore', ['abc'])
+        with self.assertRaises(UnicodeDecodeError):
+            check('strict', ['abc'])
+        check('replace', ['\ufffdabc'])
+        check('backslashreplace', ['\\x80abc'])
+        
     def test_modes(self):
         with open(TESTFN, 'wb') as f:
             # UTF-7 is a convenient, seldom used encoding