Abstract: With the rapid development and implementation of autonomous driving technology, accurate trajectory tracking for such autonomous vehicles(AVs) has become one of core techniques for fulfilling the AVs motion control in automobile industry and academic research areas. To improve the real-time and accuracy performance of trajectory tracking for the AVs, it is proposed a comprehensive linear time-varying model predictive controller(LTV-MPC) applied to a certain AV. First, a two-degree-of-freedom kinematic model of an AV is constructed in terms of vehicle kinematics principle, Next, based on this 2-DOF kinematic model of AV, a dynamic error model of vehicle's trajectory tracking system is derived using linear time-varying theory, and this model is then linearized by a successive linearization, and the design of this desirable trajectory tracking controller is transformed to a quadratic programming optimized problem in the framework of model predictive control. Finally, the effectiveness of the proposed controller is validated on a self-established test platform under various prescribed reference road trajectories, the results show that this AV with the proposed LTV-MPC can track the prescribed reference road trajectories with high speed and precision, as well as good stability for the AV under various driving conditions.