In this paper, we propose a probability based slot allocation scheme named p-persistent for vehicular networks. One vehicular node makes its decision on slot occupation according to the ratio of the slot number it has owned to the average slot number. In other words, more time slots a tagged vehicular node has owned, lower probability it will contend for a new slot with. Through this scheme the slot resource could be fully used and the fairness among users could be satisfied. Closed form of average channel utilization, slot number per user and periodic broadcast delay have been obtained. Analysis and simulation results show that the proposed p- persistent scheme has a better performance in all the three indexes listed above compared to the one- to-one scheme which is used in most of the existing studies and the pure greedy (P-G) scheme.