An　algorithm　on　concurrent　scheduling　multiple　complex　workflows　sharing　the　distributed　heterogeneous　resources　was　proposed　to　effectively　improve　the　utilization.　First,　a　reverse　heterogeneous　earliest　finish　time　(HEFT)　scheduling　policy　was　proposed,　which　can　quickly　get　the　latest　start　time　(LST)　and　sub-deadline　for　each　task.　Based　on　LST,　a　new　relative　loose　degree　metrics　was　defined　for　all　the　highest　priority　tasks　in　each　workflow.　By　comparing　them,　the　current　task　to　be　scheduled　was　selected　and　then　mapped　to　the　slot　with　the　earliest　finish　time　in　all　resources.　If　the　resources　were　not　enough,　oversaturated　workflows　can　be　rapidly　determined　in　accordance　with　sub-deadline,　and　such　workflow　scheduled　alone　by　HEFT　algorithm　with　the　minimum　idle　slot　time　is　reasonably　discarded　to　maximize　workflows　throughput.　Experimental　results　show　that　this　algorithm　has　better　comprehensive　performance　about　throughput,　waste　time　slot,　fairness　and　time　complexity　than　the　other　three　algorithms.　©　2017,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.