This paper presents a path tracking steering controller based on the model predictive control (MPC) that simultaneously minimizes lateral path tracking deviation while maintaining vehicle stability for autonomous vehicles at the limits of handling． To improve the tracking accuracy， the course direction deviation is chosen for referential state，and the steadystate sideslip is used to calculate the course direction deviation instead of using the realtime sideslip． By using the lateral force of front tire as the input of the controller directly，and linearizing the rear tire force by the affine approximation， the computational burden can be reduced． The simulation results on a CarSimSimulink demonstrate that the present controller can operate the vehicle stably at the limits of tire adhesion，and has a better performance in tracking in comparison with the traditional controller．