To enable a carrier-based unmanned aerial vehicle (UAV) to track the desired glide trajectory and safely land on the deck with the presence of system faults, this paper proposes a neural network-based adaptive sliding mode fault-tolerant control (NASFTC) method. Firstly, the dynamic model of the carrier -based UAV, the actuator fault model, the additional unknown fault model, and the control framework of the automatic carrier landing system (ACLS) were developed. Subsequently, controllers for both longitudinal and lateral channels were designed by using the NASFTC method. The controller consists of three parts: the adaptive laws for compensating the actuator faults, the RBF neural network for compensating the additional unknown faults, and the sliding mode method for ensuring overall trajectory tracking. Then, the Lyapunov function theorem was applied to carry out the stability analysis. Finally, comparative simulations under three different scenarios were conducted. The comparative results show the effectiveness of the proposed NASFTC method, which has fault-tolerant ability and can successfully control the aircraft to execute carrier landing task regardless of the actuator partial loss fault and the additional unknown fault.