This paper proposes a strategy based on model predictive control for the trajectory tracking control problem of intelligent fully line-controlled electric vehicles. By establishing a vehicle model that includes lateral, longitudinal and yaw dynamics, and comprehensively considering the actuator constraints of the distributed drive architecture, including the by-wire steering, by-wire brake and by-wire drive systems, a multi-objective optimization function with the goal of minimizing tracking error is then designed. Subsequently, the improved interior point method is adopted for a rapid solution to meet the real-time control requirements. The joint simulation results based on MATLAB/Simulink and CarSim show that this control method can effectively improve tracking accuracy and robustness in various scenarios such as straight lines, curves, and obstacle avoidance. Compared with the traditional PID control, the lateral tracking error is reduced by up to 53%, and it has good anti-interference ability and driving smoothness. This research provides a theoretical reference and engineering application basis for the precise control of fully by-wire electric vehicles.