This paper presents a new Time Division Multiple Access/Frequency Division Duplexing (TDMA/FDD) based Medium Access Control (MAC) protocol for broadband wireless networks, supporting Quality of Service (QoS) for real-time multimedia applications. It also gives the Call Blocking Probability (CBP), packet end-to-end delay and utilization analysis of different service classes, as they are most essential performance criterions in broadband wireless network assessment. The Connection Admission Control (CAC) mechanism in the proposed MAC efficiently organizes the bandwidth allocation for different service classes by means of a fairness based scheduling algorithm. In addition, the simulation model of the proposed MAC scheme is realized by using OPNET Modeler network simulator. The results of the analytical calculations for the CBPs are compared to those of the simulation of the proposed MAC, thus validity of the MAC protocol is proved.