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In Mobile WiMAX system, it is important to allocate resources appropriately in order to the efficient utilization of resources among a variety of real-time and non real-time services. Although a lot of the real-time and non real-time packet scheduling schemes in OFDMA system have been proposed, it need to be modified to apply to Mobile WiMAX system. Since Mobile WiMAX supports five kinds of service classes, it is important to take QoS constraints of each class into consideration. In this paper, we propose an efficient packet scheduling scheme to support various services by considering the QoS constraints of each class. Proposed scheme selects a service class first considering characteristics of each class and next choose an appropriate user in the selected class. Simulation results show that the proposed scheme support QoS of each class efficiently.