To improve the trajectory tracking accuracy of vehicles under conditions of strong coupling between longitudinal and lateral motions, a trajectory tracking controller was designed based on nonlinear three-step control theory and Lyapunov stability theory. This controller consists of two parts: quasi-steady-state control and state-dependent error feedback control. By controlling the equivalent longitudinal force and the front wheel steering angle of the trajectory tracking controller, it is possible to control the longitudinal and lateral motions of the trajectory tracking controller. The front wheel steering angle of the vehicle, as well as adapting system parameters, the controller overcomes the effects of coupled longitudinal and lateral motions and parameter uncertainties. Lateral motions and parameter uncertainties on trajectory tracking, guarantees precise tracking of the target trajectory. Simulation results demonstrate that the designed controller can accurately track the target trajectory under variable speed cornering conditions.