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The transmission of safety applications in VANET is clearly the top concern. However, the non-safety applications, which improve the quality of experience, as well as the efficiency of the traffic, also need to be paid more attention. In VANET, the safety applications are transmitted in control channel interval and the non-safety applications can be transmitted only in service channel interval. In this paper, we propose a priority-based multichannel MAC to support the non-safety applications in service channel interval in Vehicle-to-Infrastructure communication with the presence of roadside unit. The novel MAC also allocates service channel according to the priority and divides the vehicles, which have the same required service channel, into four priority groups to enhance the EDCA mechanism. We use the mathematical model and the simulation for evaluating the performance under the influence of velocity with a different number of vehicles in the network.