Aimed at the problems that the results of current adaptive control for Flexible Air-breathing Hypersonic Vehicle (FAHV) are capable of only achieving asymptotic error convergence to the preset envelope, and the problems of computational explosion and excessive occupancy of airborne resources remain due to online updating of neural weights, an adaptive control method is proposed for FAHV specified time convergence based on event triggering mechanism and minimum learning parameters. Firstly, an improved preset performance control mechanism is proposed which does not depend on the exact initial error value and can ensure the convergence of the specified error time. Secondly, a relative threshold event-triggered neural network for FAHV interference identification is constructed. Finally, a control algorithm of relative threshold event triggering is designed, which is capable of effectively reducing the consumption of communication resources of the closed-loop controller, and achieving good control accuracy on the basis of nonisoperiodic signal transmission. The simulation results show that the proposed method can track the height/speed reference signal on a specified time under conditions of low computing and transmission resource consumption.