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This paper concentrates on the problem of finite-time altitude and velocity tracking control for hypersonic flight vehicles that encounter unmodeled dynamics and input saturations. An adaptive neural finite-time backstepping control strategy is constructed by designing modified virtual commands and compensation signals. The minimum learning parameter algorithm based on a radial basis function is employed to approximate the unknown dynamics with low computational burden. Furthermore, an auxiliary system is established to cope with the nonlinearity caused by actuator saturation. It is concluded by a Lyapunov-based analysis that the finite-time stability is guaranteed under the developed architecture. Finally, numeral simulation is provided to demonstrate the effectiveness of the proposed controller.