With the rapid development of wireless applications, the IEEE 802.11 task group proposed the QoS- supporting enhanced distributed channel access (EDCA) MAC mechanism, which is based on the legacy IEEE 802.11 DCF, to provide service differentiation for different types of traffic flows in the networks. This paper proposes a novel Markov chain-based analytical model for the IEEE 802.11 EDCA. Unlike the existing analytical models for the EDCA, the proposed model incorporates all the three major features of the EDCA, i.e., W_min/W_max, AIFS (arbitration inter-frame space), and TXOP (transmission opportunity). With this model, the paper presents the performance evaluations of the EDCA analytically, including each priority’s transmission throughput, media access delay, packet loss rate, etc. It dose not only analyze the saturated EDCA operation case, but also analyze the non-saturated EDCA operation case. Simulation results confirm the accuracy of the model analysis. Based on the model analysis, this paper proposes an admission control scheme D-TXOP (dynamic TXOP). While making admission decision, the scheme adjusts different priorities’ TXOP parameter settings adaptively according to their QoS requirements, which greatly enhances the network capacity.