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In a task scheduling system for grid computing, most of algorithms such as reservation, backfilling, etc. are commonly used task scheduling algorithm. However, they have some insufficiencies in the system resource utilization rate and the response time due to these algorithms are insufficient in solving resource slot. In order to improve the system resource utilization rate and shorten the response time, this paper presents PB-FCFS algorithm which is a task scheduling algorithm based on FCFS and backfilling strategy for grid computing. The PB-FCFS algorithm combines backfilling and priority scheduling strategy, as well considers the resource recycling at the time of task accomplished. The simulation results show that the PB-FCFS algorithm shortens task run time and improves the system throughput rate and resource utilization rate to a certain extent.