The mobile WiMAX systems based on IEEE 802.16e-2005 provide high data rate for the mobile wireless network. However, the link quality is frequently unstable owing to the long-distance and air interference and therefore impacts real-time applications. Thus, a bandwidth allocation algorithm is required to be modulation-aware, while further satisfying the latency guarantee, service differentiation and fairness. This work proposes the Highest Urgency First (HUF) algorithm to conquer the above challenges by taking into consideration the adaptive modulation and coding scheme (MCS) and the urgency of requests. Downlink and uplink sub-frames are determined by reserving the bandwidth for the most urgent requests and proportionating the remaining bandwidth for others. Then, independently in the downlink and uplink, the HUF allocates bandwidth to every mobile station according to a pre-calculated U-factor which considers urgency, priority and fairness. Simulation results prove the HUF is modulation-aware and achieves the above three objectives, notably the zero violation rate within system capacity as well as the throughput paralleling to the best of the existing approaches.