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Trajectory and velocity tracking are currently one of the core issues in autonomous vehicle control. However, most studies deal with them separately which may cause vehicle instability under extreme conditions. In this paper, a coupled longitudinal and lateral control strategy of trajectory tracking for autonomous vehicles is presented. A lateral controller is implemented with a Linear Time-Varying MPC (LTV-MPC) to generate the front steering angle required for trajectory tracking. The side-slip angle is constrained within an interval to prevent tire saturation. Furthermore, a velocity regulation module in which the reference velocity is calculated considering the curvature of the trajectory and the lateral stability criteria is designed. A longitudinal controller is proposed to provide the traction torque with the obtained reference velocity to cope with the longitudinal velocity tracking problem.