To guarantee intelligent vehicle (IV) track preconcerted trajectory steadily, according to IV's simplified model of kinematics, IV model that based on rigid body model was established firstly. Then current and reference posture to develop the dynamic posture error of IV were selected. And state space mathematics model of IV has been constructed to track trajectory closed loop control system by the adopted posture error. Based on Backstepping control algorithm, Lyapunov function has been chosen and controller for IV lane changing and overtaking was designed. Simulation and experiment result showed that the controller designed by this method could track preconcerted trajectory quickly, it is steady and reliable during IV's lane changing and overtaking control course.