Recent research in multiple DAG workflows in heterogeneous systems have been making progress andhave solved some problems, but fail to classify the multiple DAGs, according to the demand of the performanceasked by the varied DAG workflow and also fail to address the scheduling multiple DAGs workflow with multiplepriorities submitted at different times. To solve these problems, the paper presents a new model of multiple DAGsmanagement system for multiple DAGs workflow with multiple priorities and an adjustment method to the previousFairness algorithm to solve the fairness issue in scheduling multiple DAGs with the same priorities submitted atdifferent times. In addition, the study also proposes an implementation method of the Backfill algorithm formultiple DAGs with different priorities to improve utilization rate of resource, and then, based on the new modeland the two methods, propose a hybrid strategy for scheduling multiple DAGs with multiple priorities submitted atdifferent times. These experimental results show that it is possible to meet different requirements of DAGssubmitted at different times and to improve utilization rate of a resource. In addition, the results about schedulingtwo-DAGs show a significant “Trail Ending” principle, which is valuable for academic study and application.