This article presents a trajectory following control solution for the lateral motion of an unmanned vehicle. The proposed solution is based on model predictive lateral control. The lateral motion is hard to control since it is nonlinear with large dynamics and uncertainties. By making a small angle approximation, the dynamic model can be linearized. A new bounded equivalent function based on the vehicle kinematic model and the Taylor series expansion is presented for trajectory following control solution for the lateral motion problem. The model predictive lateral control is used to ensure both strong robustness and control accuracy. Experiment results in a real environment are presented to show the effectiveness of the proposed method.