Constant Bit Rate (CBR) traffic is expected to be an important traffic source in wireless networks. Such sources usually have stringent delay and loss requirements and in many cases they should be delivered exactly as they were generated. In this paper, we propose a novel uplink packet scheduling policy for CBR traffic to support real-time applications, with strict delay requirements in IEEE 802.16 broadband wireless access (BWA) systems. Under such a scheme, the CBR traffic was characterized by its sustained traffic rate and tolerated jitter. The proposed transmit permission policy can derive sufficient conditions such that all the CBR sources satisfy their delay constraints to provide deterministic quality of service (QoS) guarantees. In addition to theoretical analysis, simulations are conducted to evaluate the performance of the proposed scheme. As it turns out, our design provides a good quality performance in the IEEE 802.16 BWA systems.