Cognitive Radios (CRs) are the most promising solution to underutilization of spectrum and spectrum scarcity problems. However, designing suitable and reliable CRs have many crucial challenges. CRs are required to utilize the spectrum holes, share the spectrum resources with other users and bound harm on primary (licensed) transmission. To overcome these problems an accurate mathematical model for the spectrum access mechanism of the CR networks is mandatory. In this paper, we propose an analytical model for CR networks, which is based on the Enhanced Distributed Channel Access (EDCA) function of the 802.11e standard. We divide the users into two different access categories (ACs), namely, primary AC (pAC) and low-priority secondary AC (sAC) users. Here, we benefit from well-known EDCA parameters (CWmin, CWmax, AIFS and TXOP) to provide this prioritization. In addition, we determine optimal values of the EDCA parameter set for CRs in order to balance the trade-off between the protection of primary users and the throughput of secondary users. We analyze a single channel environment with saturation performance of two ACs. To verify our analytical model, we also perform simulations. Results obtained from model and simulations show that the proposed channel access protocol for CRs can be reliably used in 802.11e channels without any modification in the existing Wi-Fi systems.