In this paper, an impedance control using a serial chain of spring-damper system is proposed for a vehicle platoon. For safety of the vehicle platoon, it is required to regulated the distance between each vehicle at a preassigned value even in case of vehicle model error, or moise in the measurement signal. Since the spring-damper system is physically stable and widely used to represent the interaction with the uncertain environments, it is appropriate to the longitudinal control of the vehicle platoon. By considering the nonholonomic characteristics of the vehicle motion, the lateral control and the longitudinal control of the vehicle paltoon are unified in the proposed algorithm. Computer simulation is carried out to verify the robustness against the uncertainties such as the vehicle model error and the measurement noise.