In this paper, an adaptive dynamic surface control scheme is proposed for a class of hypersonic flight vehicles with unknown elevator faults. By estimating the bounds of the fault uncertainties, the effect of the faults is successfully compensated for and each elevator is allowed to change among the healthy case and different faulty cases infinitely many times. The proposed scheme is free of the problem of explosion of complexity and is able to steer tracking errors into predefined arbitrarily small residual sets with prescribed convergence rates and maximum overshoots. Such features result in a simple flight control scheme which can be easily implemented with less computational burden, satisfactory tracking performance and high reliability. Simulation results illustrate the effectiveness of the proposed scheme.