Mobile WiMAX system provides various classes of traffic such as real-time and non-realtime services. These services have different QoS requirements and the QoS aware scheduling has been an important issue. Although many of scheduling algorithms for various services in OFDMA system have been proposed, it is needed to be modified to be applied to Mobile WiMAX system. Since Mobile WiMAX supports five kinds of service classes, it is important to take QoS characteristics of each class into consideration. In this paper, we propose an efficient packet scheduling algorithm to support QoS of each class. Proposed scheme selects a service class first considering QoS Characteristics of each class and choose an appropriate user in the selected class. Simulation results show that the proposed algorithm has better performance than the other algorithm.