Multiple Directed Acyclic Graphic (DAG) scheduling algorithms are supposed to take many factors into account, such as execution time, communication overhead, cost and fairness of all DAG. Therefore, in order to increase fairness and reduce cost, a new scheduling strategy CAFS (Communication Aware Fair Scheduling), based on CA-DAG (Communication Aware-DAG), was proposed. Also, a BD (Backward Difference) rule was introduced to optimize finish time of all DAGs. CAFS is consisted of two parts: the pre-scheduling part adopts CACO (Communication Aware Cost Optimization) to optimize the total cost, and utilizes the classical fairness algorithm to decide the sequence for scheduling. Based on the sequence the second part schedules all the DAGs using BD rule to reduce the finish time. The simulation results show that CAFS can reduce the finish time without increasing cost and guarantee the fairness, and the average execution time has been reduced by 19.82%.