A vehicle platoon is the method of grouping vehicles into platoon and driving synchronously. The vehicles in the platoon can travel safely in very small vehicle distance with the help of the mechanical and electric systems and thus, the traffic flow can be increased without any additional road construction. In this study, the interaction behavior between the vehicle platoon of three vehicles and the other vehicle is discussed. When the platoon of three vehicles overtakes the other vehicle, the vehicles in the platoon change the lane, overtake the preceding slow-travelling vehicle and changes the lane again. The vehicle velocity is controlled according to the vehicle following model (Bierley 1963, Chandler et. al. 1958, Gazis et. al. 1961, Helly 1959). The control models of vehicle velocity and behavior are defined in the mathematical model and discussed in the experiments of the robot vehicle. The results show that the model can make the platoon overtakes the other vehicle safely. In the near future, the model should be improved in order to enhance the safety and the efficiency of the vehicle platoon.