The IEEE 802.11p standard drafted to support wireless access in vehicular environments (WAVE) or vehicular ad hoc network (VANET) which uses Enhanced Distributed Channel Access (EDCA) mechanism for the contention-based prioritized Quality of Service (QoS) at the MAC layer. The EDCA mechanism defines four access categories (ACs). Each AC queue works as an independent DCF station (STA) with Enhanced Distributed Channel Access Function (EDCAF) to contend for Transmission Opportunities (TXOP) using its own EDCA parameters. This paper provides an analytical model to compute the performance of the IEEE 802.11p Enhanced Distributed Channel Access Function (EDCAF) for Vehicular Network. To develop the model the four access categories (ACs) and all the major factors that could affect the performance are considered. The relationship among the IEEE 802.11p EDCA parameters and performance matrices are derived through Markov chain based theoretical analysis. Moreover, the derived performance model is verified by simulation.