Abstract: In megacities, the number of vehicles has rapidly grown. Automatic parking, a special type of unmanned driving, has become an important technology to ease parking difficulties. Path tracking is also a core part of automatic parking. However, during automatic parking, the curvature of the reference path is very large. This poses a challenge in automatic parking and is different from that in high-speed unmanned driving. When the curvature of the reference path is large, the constraints of the system severely restrain the path tracking performance. These constraints include the limit of the steering wheel angle speed. Applying model predictive control is a good way to handle multiple constraints. Recently, a path tracking controller for automatic parking based on linear time-varying model predictive control has been reported. However, for automatic parking, the accuracy of the linearized prediction model is still insufficient. To solve this problem, a path tracking controller based on nonlinear model predictive control was proposed in this paper. This controller was compared with the controller based on linear time-varying model predictive control. The simulation environment is a combination of MATLAB/Simulink and PreScan. The simulation results show that the proposed controller could complete automatic parking with multiple constraints. After the parking was completed, the angle between the vehicle heading and the center line of the parking space was 0.0189 rad. The distance between the midpoint of the rear axle of the vehicle and the center line of the parking space was 0.1045 m. This distance was only 5.56% of the width of the vehicle body. Compared with the controller based on linear time-varying model predictive control, the proposed controller for automatic parking exhibited a higher parking precision, larger safety margin, and less parking time. In terms of real-time performance, the proposed controller could also meet the requirements for automatic parking.