Due to the dynamics of topology and resources, Call Admission Control (CAC) plays a significant role for increasing resource utilization ratio and guaranteeing users' QoS requirements in wireless/mobile networks. In this paper, a dynamic multi-threshold CAC scheme is proposed to serve multi-class service in a wireless/mobile network. The thresholds are renewed at the beginning of each time interval to react to the changing mobility rate and network load. To find suitable thresholds, a reward-penalty model is designed, which provides different priorities between different service classes and call types through different reward/penalty policies according to network load and average call arrival rate. To speed up the running time of CAC, an Optimized Genetic Algorithm (OGA) is presented, whose components such as encoding, population initialization, fitness function and mutation etc., are all optimized in terms of the traits of the CAC problem. The simulation demonstrates that the proposed CAC scheme outperforms the similar schemes, which means the optimization is realized. Finally, the simulation shows the efficiency of OGA.