In this paper, the feedback linearization scheme is applied to the control of vehicle's lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in (Liaw, D.C., Chung, W.-C. in 2006 IEEE International Conference on Systems, Man, and Cybernetics, 2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. The vehicle dynamics at the saddle node bifurcation point is derived and then decomposed as an affine nominal model plus the remaining term of the overall system dynamics. Feedback linearization scheme is employed to construct the stabilizing control laws for the nominal model. The stability of the overall vehicle dynamics at the saddle-node bifurcation is then guaranteed by applying Lyapunov stability criteria. Since the remaining term of the vehicle dynamics contains the steering control input, which might change system equilibrium except the designed one. Parametric analysis of system equilibrium for an example vehicle model is also obtained to classify the regime of control gains for potential behavior of vehicle's dynamical behavior.