diff --git a/PIL/Image.py b/PIL/Image.py
index cabc10743..bc8f91a54 100644
--- a/PIL/Image.py
+++ b/PIL/Image.py
@@ -548,10 +548,6 @@ class Image(object):
         had their file read and closed by the
         :py:meth:`~PIL.Image.Image.load` method.
         """
-        try:
-            self.fp.close()
-        except Exception as msg:
-            logger.debug("Error closing: %s", msg)
 
         # Instead of simply setting to None, we're setting up a
         # deferred error that will better explain that the core image
diff --git a/PIL/ImageFile.py b/PIL/ImageFile.py
index 94f705b3c..4146520cf 100644
--- a/PIL/ImageFile.py
+++ b/PIL/ImageFile.py
@@ -117,6 +117,16 @@ class ImageFile(Image.Image):
         # directly after open, and closes file when finished.
         self.fp = None
 
+    def close(self):
+        if getattr(self, 'map', None):
+            self.map = None
+        try:
+            if self.fp:
+                self.fp.close()
+        except Exception as msg:
+            logger.debug("Error closing: %s", msg)
+        Image.Image.close(self)
+
     def load(self):
         "Load image data based on tile list"
 
diff --git a/PIL/TiffImagePlugin.py b/PIL/TiffImagePlugin.py
index f1860e4aa..5d74296cc 100644
--- a/PIL/TiffImagePlugin.py
+++ b/PIL/TiffImagePlugin.py
@@ -944,6 +944,11 @@ class TiffImageFile(ImageFile.ImageFile):
             self.seek(current)
         return self._is_animated
 
+    def close(self):
+        if self.__fp:
+            self.__fp = None
+        ImageFile.ImageFile.close(self)
+
     def seek(self, frame):
         "Select a given frame as current image"
         self._seek(max(frame, 0))  # Questionable backwards compatibility.
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index 9913860ad..481eaa213 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -2,6 +2,7 @@ from __future__ import print_function
 import logging
 from io import BytesIO
 import struct
+import sys
 
 from helper import unittest, PillowTestCase, hopper, py3
 
@@ -499,5 +500,23 @@ class TestFileTiff(PillowTestCase):
         with Image.open(mp) as im:
             self.assertEqual(im.n_frames, 3)
 
+
+@unittest.skipUnless(sys.platform.startswith('win32'), "Windows only")
+class TestFileTiffW32(PillowTestCase):
+    def test_fd_leak(self):
+        tmpfile = self.tempfile("temp.tif")
+        import os
+
+        with Image.open("Tests/images/uint16_1_4660.tif") as im:
+            im.save(tmpfile)
+
+        im = Image.open(tmpfile)
+        im.load()
+        self.assertRaises(Exception, lambda: os.remove(tmpfile))
+
+        im.close()
+        os.remove(tmpfile)
+
+
 if __name__ == '__main__':
     unittest.main()