Scheduling　complex　DAG　(Directed　Acyclic　Graph)　scientific　workflow　in　the　distributed　heterogeneous　system　has　attracted　widespread　attention.　Recent　researches　about　multiple　DAG　workflows　in　heterogeneous　system　have　been　making　progress　and　have　solved　some　problems,　but　fail　to　address　and　to　solve　some　important　problems　of　scheduling　Deadline-Constrained　multi-DAGs　sharing　a　bounded　number　of　machines　in　a　heterogeneous　system.　In　this　work,　we　propose　a　reverse　HEFT　(Heterogeneous　Earliest　Finish　Time)　scheduling　policy,　which　can　quickly　get　the　latest　start　time　and　sub-deadline　for　each　task.　Based　on　the　latest　start　time　of　in　highest　priority　tasks　in　each　DAG,　we　define　a　new　relative　laxity　degree　metrics　for　them.　By　comparing　these　tasks＇　metrics,　the　current　task　to　be　scheduled　is　chosen　and　then　mapped　to　the　time　slot　with　the　earliest　finish　time　in　all　resources.　If　the　resources　are　not　enough,　oversaturation　can　be　rapidly　determined　in　accordance　with　sub-deadline,　and　some　DAGs　is　reasonably　discarded　and　other　resources　is　chosen.　This　multi-DAGs　scheduling　policy　select　a　relative　urgency　scheduling　task　only　by　a　simple　calculation　without　the　remaining　tasks　pre-scheduling　in　each　DAG　scheduling.　The　experimental　results　show　that　it　has　a　better　performance　than　other　three　policies　on　throughput　capacity,　waste　time　slot　ratio　and　fairness,　and　time　complexity　is　much　lower.　©　2016　IEEE.