The trajectory-tracking capability of autonomous mining trucks is critical for accomplishing transportation tasks efficiently. However, due to the diverse road surfaces and rugged terrains in open-pit mines, the existing vehicle dynamics models struggle to accurately capture the complex tire–ground interactions. As a result, conventional trajectory-tracking control methods that rely on linear vehicle dynamics models suffer from degraded tracking performance. To this end, this paper proposes a novel trajectory-tracking control framework that integrates model predictive control (MPC) with model-free adaptive control (MFAC). A warm-start strategy is employed to improve the computational efficiency of MPC, while MFAC is utilized to provide real-time compensation for the control deviations generated by MPC during the trajectory-tracking process. To validate the effectiveness of the proposed trajectory-tracking control method, co-simulations were conducted on the CarSim and MATLAB/Simulink platforms under various road conditions and driving scenarios. Simulation results demonstrate that the proposed method can effectively enhance the trajectory-tracking performance of autonomous mining trucks. For instance, under the S-condition with Class E road elevation, the proposed method achieves improvements of approximately 90.83%, 15.05%, and 71.93% in the mean error, maximum error, and root mean square error (RMSE), respectively, compared with the conventional LQR-based trajectory-tracking control method. In addition, the computation time of MPC is only 2 ms, which significantly improves the overall performance of the trajectory-tracking controller.