In order to address the significant nonlinear dynamic characteristics and limited trajectory tracking accuracy of unmanned vehicles under cornering conditions, this paper proposes a trajectory tracking control strategy based on Adaptive Model Predictive Control (AMPC). First, to enhance the accuracy of the vehicle model, an 11-degree-of-freedom vehicle dynamics model is established, incorporating pitch, roll, yaw, rotation around the Z-axis, and wheel-axis rotation. The vehicle motion equations are derived using Lagrangian analytical mechanics. Meanwhile, the tire model is optimized by accounting for the influence of vehicle attitude changes on tire mechanical properties. Based on the principles of nonlinear model predictive control (NMPC) and adaptive control, the AMPC algorithm is developed, its prediction model is constructed, and appropriate control constraints are defined to ensure improved accuracy and stability in trajectory tracking. Finally, simulations under double-lane-change and serpentine driving conditions are conducted using a co-simulation platform involving Carsim and Matlab/Simulink. The results demonstrate that the proposed controller achieves high trajectory tracking accuracy, effectively suppresses vehicle yaw, pitch, and roll motions, and enhances both the smoothness of trajectory tracking and the overall dynamic stability of the vehicle.