Unlike the traditional method of taxying, where civil aircraft reach the runway by relying on their engines, the new mode of towing taxi-out may become preferred because of its lower energy consumption, lower emissions, and higher efficiency. To improve the tracking accuracy and lateral stability of the towing system, this study used a two-level time-varying weight control method (RMPC) based on model predictive control (MPC) and fuzzy control. The tractor speed and front wheel angle were set as the control variables in the MPC controller, and the real-time lateral displacement error and yaw angle error of the tractor were set as the fuzzy control inputs. The influence of the weight matrix on the accuracy and stability of path tracking was coordinated by online optimization of the MPC objective function weight. The simulations of multiple working conditions were performed using TruckSim software in Simulink, which showed that the proposed control method can limit the lateral displacement error of the tractor and aircraft within 0.4 m, which can be reduced by 70.83% and 77.4% compared with the single MPC, respectively. Additionally, the maximum yaw angle errors of the tractor and aircraft are reduced by 76.11% and 51.31% compared with the single MPC, respectively. Furthermore, the yaw angle error of tractors can be limited to 4° and that of aircraft can be limited to 6.5°, which is an improvement of the lateral stability and driving safety for the civil aircraft towing system. The new controller may provide technical insights and support for the practical development and safe application of the towing taxi-out mode.