In this paper, we propose a cellular cognitive-radio vehicular ad hoc network (CCR-VANET) which consists of cellular network (primary network) and vehicular ad hoc network (secondary network). The two coexisting networks share the uplink spectrum of cellular network. The moving pattern of all vehicles is described as the classic Car-Following model. A cognitive carrier sense multiple access with collision avoidance (cognitive- CSMA) protocol with two-stage decision is investigated to opportunistically access the uplink spectrum. Based on this model and protocol, the transmission opportunity is derived by using stochastic geometry tools. Finally, simulation results show that, with cognitive-CSMA protocol and invariable transmission power of coexisting networks, the CCR-VANET transmission opportunity increases with the increasing of maximum received beacon power threshold, predefined carrier sensing threshold and the number of subchannels, while decreases with the increasing of the density of active primary transmitters.