Worldwide Interoperability for Microwave Access (WiMAX) based on the IEEE 802.16-2009 standard is a serious competitor of Long Term Evolution (LTE) for cellular networks providing high data rates to mobile users. To support various multimedia applications the Quality of Service (QoS) support is a crucial function. While the IEEE 802.16- 2009 standard defines five service classes to support the QoS requirements of various multimedia applications, the algorithms and especially the scheduling algorithms to enforce these requirements have not been specified for vendor differentiation. We propose a scheduling algorithm allocating resources according to the guaranteed and sustained rates of each connection, in contrast to common two layer scheduling approaches differentiating between service classes. Simulation results show that our scheduler is able to fulfill the QoS requirements of connections defined by the IEEE 802.16 standard.