Abstract: 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.