A vehicle yaw stability controller is proposed to make vehicle yaw stable in critical cornering manoeuvres in the paper. Considering vehicle body dynamics, wheel dynamics and tire nonlinear characteristics, a discrete nonlinear time-varying model is firstly constructed, with disturbances standing for tire/road forces estimation error and unmodelled dynamics. Then, the controller is proposed based on sliding mode control in backstepping control framework, in which the control input is calculated step-by-step. The stability of the system is analyzed through input-to-state stability (ISS) theory. Finally, a group of simulations is carried out with a multi-body vehicle dynamics software to evaluate the controller and the results indicate that it can maintain vehicle stable in critical cornering situation.