The IEEE 802.11 wireless standard uses the carrier sense multiple access with collision avoidance (CSMA/CA) as its MAC protocol (during the distributed coordination function period). This protocol is an adaptation of the CSMA/CD of the wired networks. CSMA/CA mechanism cannot guarantee quality of service (QoS) required by the application because of its random access method. In this study, we propose a newMAC protocol that considers different types of traffic (e.g., voice and data) and for each traffic type different priority levels are assigned. To improve the QoS of IEEE 802.11 MAC protocols over a multi-channel CSMA/CA, we have developed a new admission policy for both voice and data traffics. This protocol can be performed in direct sequence spread spectrum (DSSS) or frequency hopping spread spectrum (FHSS). For voice traffic we reserve a channel, while for data traffic the access is random using a CSMA/CA mechanism, and in this case a selective reject and push-out mechanism is added to meet the quality of service required by data traffic. To study the performance of the proposed protocol and to show the benefits of our design, a mathematical model is built based on Markov chains. The system could be represented by a Markov chain which is difficult to solve as the state-space is too large. This is due to the resource management and user mobility. Thus, we propose to build an aggregated Markov chain with a smaller state-space that allows performance measures to be computed easily. We have used stochastic comparisons of Markov chains to prove that the proposed access protocol (with selective reject and push-out mechanisms) gives less loss rates of high priority connections (data and voices) than the traditional one (without admission policy and selective reject and push-outmechanisms). We give numerical results to confirm mathematical proofs