IEEE 802.16 standard defines the air interface specifications for broadband access in wireless metropolitan area networks. Although the medium access control signaling has been well defined in the IEEE 802.16 specifications, resource management and scheduling, which play an important role in providing quality of service (QoS) performance, still remain as an open issues. We propose a scheduling algorithm at the medium access control (MAC) layer for multiple connections with diverse QoS requirements, where each connection employs adaptive modulation and coding (AMC) scheme at the physical (PHY) layer over wireless fading channels. Each connection is assigned a priority by our priority function (PF), which is updated dynamically based on its channel and QoS status. The connection which is assigned higher priority is allocated more resources. With the proposed method, we show that our scheduler provides diverse QoS guarantees and efficient use of wireless resources via simulations.