For　the　grid　workflow　of　DAG　with　strict　time　limits,　this　paper　puts　forward　a　new　algorithm　based　on　the　time　prediction　model　of　queuing　theory.　According　to　the　requirements　of　workflow　execution　time　submitted　by　users,　this　algorithm　finds　critical　path　first　and　then　obtains　the　probability　of　actual　execution　time　exceeding　the　limit　time　which　was　set　by　users　using　Little＇s　law,　and　then　selects　the　best　candidate　resources　to　execute　the　workflow　task.　The　simulation　results　show　the　effectiveness　of　the　algorithm.　©2010　IEEE.