diff -r c7f1acdd8be1 Doc/library/fileinput.rst
--- a/Doc/library/fileinput.rst	Mon Feb 01 12:47:15 2016 +0100
+++ b/Doc/library/fileinput.rst	Wed Apr 27 12:07:21 2016 -0400
@@ -188,10 +188,16 @@
    Usage example:  ``fi = fileinput.FileInput(openhook=fileinput.hook_compressed)``
 
 
-.. function:: hook_encoded(encoding)
+.. function:: hook_encoded(encoding, errors=None)
 
    Returns a hook which opens each file with :func:`codecs.open`, using the given
-   *encoding* to read the file.
+   *encoding* to read the file. *errors* is an optional string that specifies how
+   encoding and decoding errors are to be handled--this cannot be used in binary
+   mode. A variety of standard error handlers are available (listed under
+   :ref:`error-handlers`).
 
    Usage example: ``fi =
-   fileinput.FileInput(openhook=fileinput.hook_encoded("iso-8859-1"))``
+   fileinput.FileInput(openhook=fileinput.hook_encoded("iso-8859-1", errors="replace"))``
+
+   .. versionchanged:: 3.6
+      Added the *errors* keyword argument.
diff -r c7f1acdd8be1 Doc/whatsnew/3.6.rst
--- a/Doc/whatsnew/3.6.rst	Mon Feb 01 12:47:15 2016 +0100
+++ b/Doc/whatsnew/3.6.rst	Wed Apr 27 12:07:21 2016 -0400
@@ -140,6 +140,12 @@
 (Contributed by Nikolay Bogoychev in :issue:`16099`.)
 
 
+fileinput
+---------
+
+:func:`~fileinput.hook_encoded` now supports the *errors* keyword argument.
+
+
 Optimizations
 =============
 
diff -r c7f1acdd8be1 Lib/fileinput.py
--- a/Lib/fileinput.py	Mon Feb 01 12:47:15 2016 +0100
+++ b/Lib/fileinput.py	Wed Apr 27 12:07:21 2016 -0400
@@ -412,9 +412,9 @@
         return open(filename, mode)
 
 
-def hook_encoded(encoding):
+def hook_encoded(encoding, errors=None):
     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	Wed Apr 27 12:07:21 2016 -0400
@@ -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 +892,26 @@
         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:
+            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
diff -r c7f1acdd8be1 Misc/ACKS
--- a/Misc/ACKS	Mon Feb 01 12:47:15 2016 +0100
+++ b/Misc/ACKS	Wed Apr 27 12:07:21 2016 -0400
@@ -534,6 +534,7 @@
 Lars Gustäbel
 Thomas Güttler
 Jonas H.
+Joseph Hackman
 Barry Haddow
 Philipp Hagemeister
 Paul ten Hagen
diff -r c7f1acdd8be1 Misc/NEWS
--- a/Misc/NEWS	Mon Feb 01 12:47:15 2016 +0100
+++ b/Misc/NEWS	Wed Apr 27 12:07:21 2016 -0400
@@ -166,6 +166,9 @@
 Library
 -------
 
+- Issue #25788: fileinput.hook_encoded() now supports an errors argument
+  for passing to open.
+
 - Issue #26202: copy.deepcopy() now correctly copies range() objects with
   non-atomic attributes.