This paper considers the characteristics of the resource scarcity and the frequent handoff in LEO systems. In view of more types of service and more users, it is much more significant to design the new admission control scheme for LEO satellite networks. The overall utility is taken as the standard, and the utility function is used to construct the game model. When the free channel resource is not enough, the channel and the service have to play a game to decide whether degrade or not, and figure out the degradation resource if the degradation is needed. Simulation results show that, by using this scheme, the overall utility and the resource utilization are greatly improved.