Generally speaking, lateral steering control method which ensures a good performance in tracking quality and handle quality simultaneously for autonomous vehicle is a changeling task. In order to keep the vehicle to stay safe when facing with severe situations such as an emergency lane change, a switched MPC lateral steering controller, which is on the basis of the stability feature of the vehicle, is presented in this paper. First, a MPC steering controller based on the 3DOF nonlinear vehicle model is derived, a comparative study of different vehicle models for MPC prediction are made. It proves that the presented MPC controller based on 3DOF nonlinear vehicle model possesses an advantage of balancing the conflicts between the tracking quality and handling quality of the vehicle. Further, a linear-piecewise switch function which is based on the vehicle stability feature to assess the vehicle handling quality is proposed, and a nonlinear observer for tire sideslip angle is built and validated to obtain the vehicle stability feature online. The switched MPC steering controller is then established with the switch function. The effectiveness of the switched MPC steering controller is validated by the DLC maneuver with a moderate speed and higher speed respectively. It proves that, when facing with an emergency lane change in high speed, the presented controller could track the target path well, and obtain a good performance of handling quality as well.