An efficient scheduling algorithm can enhance the quality of service (QoS) provided by IEEE802.16e mobile WiMAX. In this paper, a cross-layer scheduling algorithm based on genetic algorithm (CLSAGA) under the network utility maximization (NUM) concept is proposed to allocate resources for each service flow. The real coded genetic algorithm is employed to solve NUM optimization problem. Adaptive modulation and coding (AMC) scheme and QoS category index of each service flow jointly decide the weights of utility functions to calculate the scheduling scheme of medium access control (MAC) layer. Simulation results show that this approach guarantees the QoS requirements and balances priorities of the mobile stations.