In this paper, an adaptive neural network based dynamic surface sliding-mode control (ANDSSMC) scheme is proposed for the aircraft flight path angle system with external disturbances and parameters uncertainties. By using the minimum learning technology, only one parameter needs to be updated online at each design step, so that the controller is much simpler and the computational burden can be greatly reduced. The tracking error constraint functions are introduced to ensure the tracking error keep in the prescribed boundaries, and the tracking performance is improved. By combing dynamic surface controller design technique with sliding mode method, the proposed controller can not only eliminate the problem of "explosion of complexity" existing in traditional backstepping approach but also improve the robustness of the system. By using the Lyapunov theory, it is proved that all signals of the closed- loop system are uniformly ultimately bounded and the tracking performance has been achieved. Finally, the simulation results are carried out to validate the effectiveness of the proposed control algorithm.