This paper focuses on the fault-tolerant control problem of air-breathing hypersonic vehicles (AHVs) by using the adaptive method. A tractable control-oriented model is first derived for AHVs with uncertain parameters, flexible dynamics as well as sensor and actuator faults, which gathers the concerned uncertain factors in a processable linearly parameterised form. The followed design combines the classic dynamic surface control with a novel bound estimation mechanism to circumvent the 'explosion of complexity' introduced by the recursive procedure and the time-varying uncertain parameters involved in the parameterised model. The resulting adaptive controller also compensates for the possible saturation of fuel-to-air equivalency ratio and the inevitable quantisation of elevator deflection angle, along with a relatively simple algorithm. Finally, the performance of the proposed controller is evaluated by a simulation study.