A multiserver multiqueue (MSMQ) based scheduling system of the Service Grid system and a modeling and analysis method based on Stochastic Petri Net (SPN) are proposed. Due to the cost and resources consumed are different for difference Grid Service requests, the multiple priority queues are designed in the grid scheduler of the scheduling system. In order to promote the throughput, we propose a priority-based Advanced Shortest Expected Delay First scheduling algorithm (P-ASED) which is consists of two steps: the first step is request selecting according to the priority of requests; and the second step is request dispatching according to the weighted average of the expected delay and relative queue length of service nodes. The simulation experiments verify that the proposed MSMQ-based scheduling system and the P-ASED algorithm can schedule the service request according to the priority and promote the throughput of the Service Grid system.