This work introduces a Model Predictive Control (MPC) path tracking controller, which is developed to boost robustness, tracking precision, and vehicle stability when navigating high-speed and high-curvature driving scenarios. First, a 3-degree-of-freedom (3-DOF) dynamic model of the vehicle is established to serve as a reference. Next, a linear time-varying MPC control algorithm is formulated, with constraints on yaw rate, lateral velocity, and road boundary conditions taken into account; a comprehensive performance metric that balances tracking accuracy and control smoothness is also defined. Third, the time-domain parameters of the MPC framework are optimized using an improved genetic algorithm. Finally, the effectiveness and accuracy of the proposed controller are validated via co-simulation experiments conducted on the Matlab/Simulink and Carsim platforms. Simulation results demonstrate that the controller exhibits excellent robustness: the peak lateral tracking error is only 0.05 m on high-friction roads and 0.12 m on low-friction roads, with a maximum heading error of 0.15°. Additionally, the vehicle’s dynamic stability is notably enhanced: the yaw rate is reduced by 9.6% and 15.7% on high- and low-adhesion roads, respectively, while the sideslip angle is decreased by 13.2% and 18.4% under the same conditions.