This paper presents an analytical model of IEEE 802.11e enhanced distributed channel access (EDCA) with a virtual collision handler (VCH). The proposed analytical model provides different access categories (ACs) for supporting the quality of service (QoS) of differentiated services by using different contention window (CW) sizes and arbitration interframe space (AIFS) values in EDCA. The proposed model considers a network of stations, each of which has multiple queues and a VCH for different ACs. Based on the proposed model, we analyze the throughput and delay performance of the EDCA with four different ACs and investigate the effect of the VCH by considering two VCH schemes. The analytical and simulation results show that the proposed analytical model is very accurate for various CW sizes and AIFS values.