Road capacity, traffic safety, and energy efficiency can be extremely improved by forming platoons with a small intra-vehicle spacing. Automated controllers obtain vehicle speed, acceleration, and position through vehicular ad hoc networks (VANETs), which allows the performance of platoon communication to make a significant impact on the stability of the platoon. To the best of our knowledge, there is not much research relating to packet delay and packet dropping rate of platoon communication based on the IEEE 802.11p broadcasting. In this paper, we introduce platoon structure model, vehicle control model, and communication model for a single platoon scenario. By utilizing Markov process and M/G/1/K queuing theory, we put forward an analytical model to assess the property of intra-vehicle communication. The analytical model is validated by simulations and the influence of communication parameters on intra-vehicle communication performance are discussed. In addition, the experimental results demonstrate that the IEEE 802.11p-based intra-vehicle communication guarantee the stability of platoon.