diff --git a/Lib/test/test_zipfile.py b/Lib/test/test_zipfile.py
index ed800c5..55cfaa9 100644
--- a/Lib/test/test_zipfile.py
+++ b/Lib/test/test_zipfile.py
@@ -688,6 +688,16 @@
         # quickly.
         self.assertRaises(IOError, zipfile.ZipFile, TESTFN)
 
+    def test_empty_file_raises_BadZipFile(self):
+        f = open(TESTFN, 'w')
+        f.close()
+        self.assertRaises(zipfile.BadZipfile, zipfile.ZipFile, TESTFN)
+
+        f = open(TESTFN, 'w')
+        f.write("short file")
+        f.close()
+        self.assertRaises(zipfile.BadZipfile, zipfile.ZipFile, TESTFN)
+
     def testClosedZipRaisesRuntimeError(self):
         # Verify that testzip() doesn't swallow inappropriate exceptions.
         data = io.BytesIO()
diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index 6357b94..79ca152 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -200,7 +200,10 @@
     # Check to see if this is ZIP file with no archive comment (the
     # "end of central directory" structure should be the last item in the
     # file if this is the case).
-    fpin.seek(-sizeEndCentDir, 2)
+    try:
+        fpin.seek(-sizeEndCentDir, 2)
+    except IOError:
+        return None
     data = fpin.read()
     if data[0:4] == stringEndArchive and data[-2:] == b"\000\000":
         # the signature is correct and there's no comment, unpack structure
diff --git a/Misc/NEWS b/Misc/NEWS
index d335bfd..ec4fa86 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -61,6 +61,9 @@
 Library
 -------
 
+- Issue #6511: ZipFile now raises BadZipfile (instead of an IOError) when
+  opening an empty or very small file.
+
 - Issue #7556: Make sure Distutils' msvc9compile reads and writes the
   MSVC XML Manifest file in text mode so string patterns can be used 
   in regular expressions.