The traditional research on the capacity of the Vehicular Ad Hoc Networks (VANETs) mainly lacks realistic models mimicking the behaviors of vehicles and the MAC protocol applied by IEEE 802.11p. To overcome these drawbacks, in this paper, the network transmission capacity analysis for VANETs is carried out from the perspective of the spatial geometric relationship among different vehicles. Specifically, the transmission scheme in this system is set to mimic enhanced distributed channel access (EDCA) protocol, in which the division of priorities is taken into account both the data type and the transmission distance requirement. Meanwhile, the moving pattern of vehicles is described as the classic car-following model according to realistic characteristics of VANET, and the propagation channel is modeled as a combination of large-scale path-loss and small-scale Rayleigh fading. Based on this model, the transmission opportunity under EDCA protocol is quantified and compared with that of CSMA/CA, and then the outage probability is calculated under the worst interfered scenario. Finally, the transmission capacity is thereby calculated and verified by the simulation results.