Grid computing has emerged as an important new field, distinguished from conventional distributed computing by its focus on large-scale resource sharing, innovative applications, and high-performance orientation. A Grid integrates and coordinates resources and users that live within different control domains with the goal of delivering non-trivial quality of service (QoS). Consequently, task management and scheduling is of central importance for the Grid-based systems. In this paper, we model the task dispatching and selecting on the distributed Grid computing system by a multiserver multiqueue (MSMQ) model, and propose a modeling and analysis technique based on Stochastic Petri Net (SPN) methods. An approximate analysis technique is also proposed to reduce the complexity of the model.