Worldwide Interoperability for Microwave Access (WiMAX) mobile communication systems deliver all services through the Internet Protocol. Therefore, an important and crucial part of such systems is the Quality of Service (QoS) support to fulfill the needs of real-time applications. The underlying IEEE 802.16 standard specifies the QoS entities and signaling, but all algorithms are left open for vendor differentiation. In this paper, we propose a Mobile WiMAX QoS concept. It consists of a QoS aware traffic shaping and scheduling algorithm. In contrast to other proposals, our scheduling algorithm does not differentiate between service classes, but between the guaranteed and sustained traffic rate specified by the IEEE 802.16-2012 standard. Our Two-Rate-Based Scheduler (TRBS) additionally accomplishes fairness based on radio resources between users after fulfilling guaranteed demands. Large scale simulation results show that our TRBS algorithm satisfies the QoS requirements of real-time flows. The comparison to Proportional Fair scheduling by means of the number of supported VoIP users and system goodput reveals a significantly better system performance of our scheduling algorithm in highly loaded cells.