In vehicular ad-hoc network (VANET), the reliability of communication is associated with driving safety. However, research shows that the safety-message transmission in VANET may be congested under some urgent communication cases. More spectrum resource is an effective way to solve transmission congestion. Hence, we introduce cognitive radio (CR) enabled VANET (CR-VANET), where CR device can detect possible idle spectrum for VANET communications and assist to timely broadcast safety-message. Given high-speed mobility of vehicles and dynamically-changing availability of channels, a novel prediction algorithm is proposed to pick out the channel with the greatest probability of availability, which can meet the quality of service (QoS) requirement of urgent communications and effectively avoid conflict with licensed users. Specifically, the spatiotemporal correlations among historical spectrum sensing data are exploited to form prior knowledge of channel availability probability, and Bayesian inference is used to derive posterior probability of channel availability. Comparing with other spectrum detection methods, the proposed algorithm has more than 8 percent detection performance improvement at false alarm probability 0.2, and thus can avoid access conflict with licensed users dramatically. Furthermore, the proposed algorithm always has larger packet reception probability (PRP) and lower transmission delay compared with conventional VANET broadcasting. Hence, the proposed algorithm can improve reliability of safety-message transmission and enhance driving safety significantly.