An anti-windup controller modification is implemented in control system design for a model of the longitudinal dynamics of an air-breathing hypersonic vehicle. Anti-windup control allows the input constraints to be considered explicitly in the design of linear controllers to track a reference trajectory for the vehicle velocity, altitude, and angle of attack. The presence of anti-windup alleviates the need of keeping large penalties on the magnitude of the control input to avoid the occurrence of saturation. This, in turn, allows tighter tuning of the controller gains to obtain faster and more accurate trajectory tracking. The paper employs recent developments in anti- windup design to deal with the presence of exponentially unstable dynamics, which are typically encountered in air-breathing vehicle models. Simulation results on a fully nonlinear model are presented to validate the controller design.