The management of resources and scheduling computations is a challenge in a grid,because the resources are geographic distributed,heterogeneous,dynamic.This article uses the Random Advanced Petri Net model to describe scheduling problems and improve Sufferage Algorithm.It considers the time used to access and transfer the input/output data before/after the execution,and the QoS requirements of users while pursuing the minimum completing time.The results of Ameliorate Sufferage algorithm can satisfy the QoS requirements of grid users.