Multiplayer, real-time games are a kind of soft real-time systems because a game server has to respond to requests from many clients within specified time constraints. Client events have different timeliness and consistency requirements according to their nature in the game world. These requirements lead to different priorities on CPU processing. Events can be divided into different groups, depending on their consistency degree and priority. To handle these events with different priority and meet their timing constraints, we propose a priority-based group task scheduling policy in this paper. The number of clients or events requested by each client may be increased temporarily. In the presence of transient overloading, the game server needs to allocate more CPU bandwidth to serve an event with the higher priority level preferentially. The proposed scheduling policy is capable of enhancing real-time performance of the entire system by maximizing the number of events with higher priority completed successfully within their deadlines. The performance of this policy is evaluated through extensive simulation experiments.