As the research of Grid goes on, users demand increasingly high quality of task completion and highquality scientific computing tasks continue to increase. This renders QoS a new problem that is to be considered in the Grid scheduling algorithm. In this paper, a Grid tasks scheduling strategy based on QoS priority grouping is proposed. In this algorithm, the deadline property of task, acceptation rate of tasks and makespan of systems are comprehensively considered. And QD-Sufferage, a Grid task scheduling based on task priority grouping and deadline, is presented subsequently. The experiments show that the algorithm overweighs traditional algorithms a lot in makespan, throughout parameters.