In order to improve the trajectory tracking accuracy and stability of the aircraft in the traction process, taking the four-wheel steering aircraft traction system as the research object, the kinematics model of the aircraft traction system is established, and the four-wheel steering trajectory tracking control method of the tractor based on the model predictive control is proposed. Taking the double lane changing condition as the reference trajectory, the motion control simulation model of the aircraft traction system is built in Matlab/Simulink, and the four-wheel steering trajectory tracking controller is established by combining the speed of the tractor and the angular distribution relationship of the four wheels. The controller is compared and analyzed with the traditional PID control to derive the superiority of the controller, and the tractor four-wheel steering and front-wheel steering trajectory tracking controllers are simulated and compared and analyzed at the speeds of 1.5 m/s, 3 m/s and 4 m/s, respectively. The designed controller is simulated and verified by changing the initial positional attitude of the aircraft traction system at a speed of 1.5 m/s. The results show that at three different speeds, the airplane lateral error, the heading angle error, and the tractor heading angle error under the four-wheel steering trajectory tracking control of the tractor are smaller than those under the front-wheel steering trajectory tracking control. In the case of initial deviation, the four-wheel steering trajectory tracking controller can enable the aircraft to complete the correction of the initial deviation in time, reduce the trajectory tracking error, and at the same time improve the stability of the aircraft's traction system in the driving process.