The roll of an autonomous vehicle during a fast-turning process can significantly increase the inherent nonlinear dynamics, and consequently lead to an obvious decrease of trajectory tracking accuracy and stability. A trajectory tracking controller based on a nonlinear model predictive control (NMPC) considering vehicle rolling motion is thus developed for addressing this critical issue in practice. With Lagrangian analytical mechanics and vehicle dynamics analysis methods, nonlinear vehicle models considering roll factors is established, including vehicle body dynamics model and a modified "Magic Formula" tire model. Based on this novel vehicle model, a Nonlinear Model Predictive Controller (NMPC) is constructed, and the linear and nonlinear constraints of the controller are ensured such that the motion of the vehicle is within the stable region. Based on the joint simulation platform of Carsim and Simulink, the trajectory tracking control effect in high-speed serpentine motion and double-shift line motion is verified. Simulation results show that the controller designed in this paper effectively improves the tracking accuracy and vehicle state stability in high-speed turning situations.