diff --git a/Lib/test/test_zipfile.py b/Lib/test/test_zipfile.py
index d4bb4d2..b17f857 100644
--- a/Lib/test/test_zipfile.py
+++ b/Lib/test/test_zipfile.py
@@ -701,6 +701,16 @@
         # 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 test_closed_zip_raises_RuntimeError(self):
         # Verify that testzip() doesn't swallow inappropriate exceptions.
         data = io.BytesIO()
diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index de06d82..0cfa37e 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 aa4cfd9..a60f3b2 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -956,7 +956,10 @@
 Library
 -------
 
-- Issue #6545: Removed assert statements in distutils.Extension, so the 
+- Issue #6511: ZipFile now raises BadZipfile (instead of an IOError) when
+  opening an empty or very small file.
+
+- Issue #6545: Removed assert statements in distutils.Extension, so the
   behavior is similar when used with -O.
 
 - unittest has been split up into a package.  All old names should still work.