In this paper, we propose a vehicle-to-infrastructure (V2I) communication system that utilizes a smart antenna technology to increase service coverage and system capacity. In the proposed V2I communication system, the infrastructure forms multiple directional beams to detect, in the shortest possible time, vehicles that have newly arrived within the area of its service coverage. We also propose a contention-based channel access procedure in the proposed V2I communication system. During channel access, collisions occur when more than two vehicles select the same mini-slot to transmit an access signal to an infrastructure. To solve this problem, we propose efficient channel access schemes with different approaches. Through performance analysis and simulation results, we show that our proposed schemes can contribute to reduce the number of collisions that occur during channel access. In addition, we also show that the proposed V2I communication system can increase the service coverage compared to a conventional V2I communication system that uses omni-directional antenna.