Abstract: MapReduce has been widely used in data-intensive applications;it has several advantages,such as good programming interface,high availability and fault tolerance.It is suitable for distributed processing on large-scale data,for instance,network analysis,bioinformatics and high-performance computing.In shared cluster,there are many researches on scheduling issue.However,in multi-processers nodes,the scheduling method based on priority constrain which conclude multi MapReduce tasks is uncommon.This paper provides a scheduling method based on priority constrain which conclude multi MapReduce tasks. Workload applications have a priority dependency constraint (which can be represented by DAG).Meanwhile,for the limited bandwidth of the low cost of data transmission,data dependence limit should be concluded in the scheduling system.The proposed algorithm can provide:MapReduce task scheduling with precedence constraints;by considering the data dependencies restrict the data pre-placement strategy to reduce transmission costs.