For the longitudinal maneuver mission of air-breathing hypersonic vehicles, this paper develops an adaptive control strategy based on multiple Lyapunov function method. A switched model is applied to describe vehicle dynamics within the admissible range of velocity and altitude, as well as to make a proper tradeoff between modelling accuracy and design complexity. In comparison to the existing common Lyapunov function-based control, the proposed control is less conservative and requires relatively small input by directly identifying uncertain parameters in the switched model. Moreover, the tedious analytical differentiations in back-stepping are bypassed by the integration of dynamic surface control and online differentiator technique. A simulation study is provided to verify the proposed control.