According　to　the　dependence　and　deadline　of　the　grid　workflow　tasks,　the　effective　degrees　and　MIPS　of　the　grid　resources,　a　new　algorithm　called　the　priority　tasks　scheduling　algorithm　based　on　the　grid　resource　prediction　is　presented.　The　algorithm　uses　DAG　to　find　the　critical　path,　obtain　the　deadline　of　every　task　and　compute　their　PRI　(priority).　The　algorithm　takes　the　below　problems　into　consideration:　the　request　of　user,　the　type　of　resources　and　re-scheduling　of　failed　tasks.　The　result　shows　that　the　algorithm　is　effective.