This paper discusses a model-free control design for a class of vehicle systems. A fuzzy logic steering control (FLSC) is designed for trajectory tracking of a wide class of vehicles. The FLSC system utilizes the hierarchical character of the system to reduce the rule base size, thus reducing its complexity. The stability analysis of this control system is addressed. The Lyapunov direct method is utilized to derive stability criteria to guarantee the convergence of the trajectory error, based on our proposed Lyapunov function. Satisfying the criteria guarantees the vehicle to converge to the desired linguistic zero error region. Simulations are given with a skid-steer and Ackermann vehicle model to demonstrate the FLSC’s capability to track the desired trajectory and converge to the linguistic zero error region. Our approach can be used for trajectory tracking problems on a wide range of vehicles. It enables straightforward tuning of the controller’s behavior.