Nonlinear Model Predictive Control (NMPC) has attracted growing attention in vehicle motion control. This paper proposes an NMPC-based trajectory tracking controller for autonomous vehicles that incorporates body roll dynamics to mitigate the accuracy loss and instability caused by increased nonlinearities during high-speed cornering. Using Newton’s second law and vehicle kinematics, and considering body roll geometry together with load transfer effects, a nonlinear vehicle dynamics model is established, comprising vehicle body dynamics and an improved “Magic Formula” tyre model. On this basis, an NMPC predictive model with appropriate linear and nonlinear constraints is developed to keep the vehicle’s operating states within a feasible region. Co-simulations on a CarSim-Simulink platform under high-speed cornering and double lane-change scenarios show that the proposed controller effectively improves trajectory tracking accuracy and vehicle state stability.