This paper investigates the design of an adaptive MPC trajectory tracking algorithm and controller for electric vehicles to address the issue of increased trajectory tracking errors caused by changes in vehicle dynamic parameters at different speeds in standard MPC controllers. Firstly, an adaptive trajectory tracking algorithm based on MPC was designed and compared to evaluate the impact of different prediction time domains on trajectory tracking at different vehicle speeds. Secondly, it solves the problem of reduced trajectory tracking adaptability at different speeds when using constant prediction time domain. Finally, a variable predictive time-domain trajectory tracking controller was designed, which can adapt to changes in vehicle speed. Through joint simulation using CarSim/MATLAB/Simulink, the results show that the improved trajectory tracking controller has excellent control accuracy and stability at different vehicle speeds.