A　priority　calculating　method　was　proposed,　in　which　the　grid　workflow　applications＇　priority　vector　was　calculated　by　the　users＇　identity,　credit,　urgency　and　dependency　of　grid　applications　in　the　workflow.　The　full　priority　scheduling　algorithm　generates　the　scheduling　list　according　to　the　priority　vectors,　and　only　the　application　which　has　the　highest　priority　can　be　submitted　while　the　non-absolute　priority　scheduling　algorithm　schedules　several　independent　grid　applications　so　as　to　compensate　the　parallelism　problem　of　the　full　priority　scheduling　algorithm.　Experiments　show　that,　when　the　grid　has　fewer　available　resources　or　the　performance　discrepancy　of　the　resources　is　much　higher,　the　full　priority　scheduling　algorithm　ensures　the　workflow　applications　that　have　high　priority　to　be　scheduled　firstly;　and　when　the　grid　contains　more　resources　that　have　the　same　performance,　the　non-absolute　priority　scheduling　algorithm　avoids　largely　increasing　of　the　workflow＇s　makespan　caused　by　resources　waste.