Based on the non-linearities and time-varying property of lateral kinematics model for intelligent vehicles, an improved overtaking model based on Bezier curve was proposed and a single neuron PID tracking control strategy was designed for overtaking. Compared with conventional path tracking methods, this controller only needs the angle between the horizontal plane and the vertical plane and the horizontal distance without considering the strict curve tracking, which is more similar to human driving. Of the 120km's test, the total overtaking count was 25, success rate was 92%. Test results show that the improved model could reflect the overtaking process, and prove the correctness and feasibility of this controller.