IEEE 802.11, the standard of wireless local area networks (WLANs), allows the coexistence of asynchronous and time-bounded traffic using the distributed coordination function (DCF) and point coordination function (PCF) modes of operations, respectively. In order to reach better quality-of-service (QoS) requirements for real-time application, the 802.11 E task group was formed and has proposed EDCA (Enhanced Distributed Channel Access) for the contention period and HCCA (HCF Controlled Channel Access) for the contention-free period in HCF (Hybrid Coordination Function) to enhance the original IEEE 802.11 medium access control (MAC) protocol. However, the problem of choosing the right set of MAC parameters and strict QoS mechanism to provide predictable QoS in IEEE 802.11 E Wireless LANs remains unsolved. In this paper, we propose a novel non-preemptive priority based access control scheme for the IEEE 802.11E standard. Under such a scheme, modifying the EDCA access method in the contention period supports multiple levels of priorities such that user mobility can be supported in wireless LANs. In the contention-free period, the CBR (Constant Bit Rate) session was characterized by its traffic rate and tolerable jitter, and the maximum delay will be forecasted. Hence, the proposed transmit-permission policy for HCCA access method can derive sufficient conditions such that all the CBR sources satisfy their time constraints to provide deterministic QoS guarantees. In addition, our proposed scheme is provably optimal for CBR traffic in that it gives minimum average access delay for each packet. In addition to theoretical analysis, simulations are conducted to evaluate the performance of the proposed scheme. As it turns out, our design indeed provides a good performance in the IEEE 802.11 E WLANs environment.