Considering the bounded external disturbance and controller uncertainties of the morphing aircraft, the non-fragile finite-time robust controller design problem is investigated. Firstly, the longitudinal motion of morphing aircraft is modeled as a class of switched systems. Since the properties of each subsystem may be different, the multiple Lyapunov functional method and mode-dependent average dwell time method are combined to guarantee the finite-time boundedness and robust performance of the system, which is less conservative. In addition, the non-fragile robust controller based on state-feedback is proposed to overcome the influence caused by the inherent and unavoidable imprecision of the controllers. The sufficient existing conditions and solutions of the controllers are given in the form of linear matrix inequalities. Simulation results show the superiority and effectiveness of the proposed method.