To improve the problems of poor trajectory specification, unsecured safety, and unsmooth paths planned by the artificial potential field (APF) in the high-speed overtaking state of intelligent vehicles. The lane-changing gravitational potential field was designed to guide the smart vehicle to change lanes to ensure the normality of the lane-changing trajectory. An obstacle vehicle repulsive potential field with an anisotropic distribution structure was constructed to improve the safety of lane changing, and the road centerline repulsive potential field with a steering notch and design the smoothing cost function was established to optimize the planned trajectory points to make the planned path smoother. The path tracking controller based on linear quadratic regulator (LQR) was designed to track the planned path. Through the joint simulation of Simulink and Carsim, the results show that the improved APF algorithm can plan a more reasonable path, and the tracking error of the designed LQR path tracking controller tends to be close to zero, which can better control the vehicle to complete the overtaking lane change.