diff --git a/tornado/web.py b/tornado/web.py
index <HASH>..<HASH> 100644
--- a/tornado/web.py
+++ b/tornado/web.py
@@ -1877,9 +1877,10 @@ class StaticFileHandler(RequestHandler):
         ims_value = self.request.headers.get("If-Modified-Since")
         if ims_value is not None:
             date_tuple = email.utils.parsedate(ims_value)
-            if_since = datetime.datetime(*date_tuple[:6])
-            if if_since >= self.modified:
-                return True
+            if date_tuple is not None:
+                if_since = datetime.datetime(*date_tuple[:6])
+                if if_since >= self.modified:
+                    return True
 
         return False
Add check in case parsedate failed.

email.utils.parsedate returns None if failed to parse date, add a check
to handle that.