diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -744,12 +744,18 @@
         else:
             return self.readsparse(size)
 
+    def __read(self, size):
+        buf = self.fileobj.read(size)
+        if len(buf) != size:
+            raise ReadError("unexpected end of archive")
+        return buf
+
     def readnormal(self, size):
         """Read operation for regular files.
         """
         self.fileobj.seek(self.offset + self.position)
         self.position += size
-        return self.fileobj.read(size)
+        return self.__read(size)
 
     def readsparse(self, size):
         """Read operation for sparse files.
@@ -777,7 +783,7 @@
             realpos = section.realpos + self.position - section.offset
             self.fileobj.seek(self.offset + realpos)
             self.position += size
-            return self.fileobj.read(size)
+            return self.__read(size)
         else:
             self.position += size
             return NUL * size
@@ -2336,8 +2342,20 @@
             self.firstmember = None
             return m
 
+        # Advance the file position if needed.
+        size = self.offset - self.fileobj.tell()
+
+        if size < 0:
+            self.fileobj.seek(0)
+            size = self.offset
+
+        while size > 0:
+            s = min(size, RECORDSIZE)
+            if len(self.fileobj.read(s)) != s:
+                raise ReadError("unexpected end of archive")
+            size -= s
+
         # Read the next block.
-        self.fileobj.seek(self.offset)
         tarinfo = None
         while True:
             try:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -285,6 +285,25 @@
                     "ignore_zeros=True should have skipped the %r-blocks" % char)
             tar.close()
 
+    def test_premature_end_of_archive(self):
+        for size in (512, 600, 1024, 1200):
+            with tarfile.open(tmpname, "w:") as tar:
+                t = tarfile.TarInfo("foo")
+                t.size = 1024
+                tar.addfile(t, StringIO.StringIO("a" * 1024))
+
+            with open(tmpname, "r+b") as fobj:
+                fobj.truncate(size)
+
+            with tarfile.open(tmpname) as tar:
+                with self.assertRaises(tarfile.ReadError):
+                    for t in tar:
+                        pass
+
+            with tarfile.open(tmpname) as tar:
+                with self.assertRaises(tarfile.ReadError):
+                    tar.extractfile(tar.next()).read()
+
 
 class MiscReadTest(CommonReadTest):
     taropen = tarfile.TarFile.taropen