In recent years, the problem of spectrum mobility in Cognitive Radio (CR) Networks has been widely investigated. In order to fully utilize spectrum resources, many spectrum handoff techniques based on game theory have been proposed, but most studies only concern how to achieve better payoffs for users, without paying much attention to the Quality of Service (QoS). Thus, we propose a new channel switching model based on game theory, using a prioritized approach to meet the diverse needs of users, such as bandwidth, delay, and jitter. Once the Nash equilibrium is achieved, our model will provide different QoSes by setting different priorities to different users. We also propose two acceleration methods to reach the Nash equilibrium more quickly. Finally, we evaluate the performance of the proposed schemes using real channel availability measurements. Experiments results show that our model can provide differentiated services and our algorithm is guaranteed to reach an approximate Nash equilibrium within polynomial time.