The objective of this paper is to examine the issues of low accuracy and poor stability in vehicle trajectory tracking under a transverse controller, with a view to investigating the transverse and longitudinal control of vehicle trajectory tracking. Firstly, an MPC transverse controller based on a single-point pre-scan model is constructed. Secondly, a longitudinal controller with PID as the upper layer and vehicle dynamics as the lower layer is constructed. Once more, GA is applied to optimise the parameters of the MPC controller globally offline. Finally, a classical double-shift line trajectory tracking simulation model has been constructed using MATLAB and Carsim software. The results demonstrated that the average deviation of transverse displacement was reduced by 16.76%, and the average transverse angular velocity was reduced by 6.79%, under MPC+PID controllers relative to MPC control. Following the implementation of GA optimization, significant enhancements have been made to the performance of the MPC+PID controllers.