Self-driving vehicles, also known as Autonomous Vehicles (AVs), are steadily becoming very popular due to their huge benefits. They can improve safety, convenience and transport interconnectivity as well as reduce congestion, pollution and emissions. The generation of the comfort motion signal for AVs passenger via the calculation of accurate motion cues with lower motion discomforts is important to promote the adoption of Avs in society. Model predictive control (MPC) is currently used in AVs for tracking the motion signal with good accuracy. However, the higher efficiency of MPC is directly related to the right setting of the weights. In addition, the tracking of time-varying longitudinal velocity is not possible without using linear time-varying (LTV) MPC. In this study, an LTV MPC system is designed and developed as a highly efficient motion tracking mechanism for AVs to reduce the motion tracking error and motion discomfort. In addition, biogeography-based optimisation (BBO) is employed to determine the optimal weights of the LTV MPC controller, which further reduces the motion tracking error and increases the motion comfort for users. The empirical study demonstrates that a BBO-tuned LTV MPC controller decreases the mean square error of motion tracking by 4.79% as compared with that of a manually-tuned version. Moreover, the mean square errors of the lateral deviation and relative yaw decrease by 91.22% and 19.14% as compared with those from a manually-tuned LTV MPC counterpart, respectively.