In this paper, considering a class of nonlinear systems with full state constraints and actuator faults, an adaptive neural network output feedback fault-tolerant control algorithm with prescribed performance is proposed. A state observer is constructed to solve the unmeasurable states problem. Unknown nonlinear functions in the systems are approximated by radial basis function neural networks (RBF NNs) . By introducing the nonlinear mapping, the systems with state constraints are transformed into novel systems without state constraints. Moreover, a novel performance function is utilized to guarantee that the tracking error converges within a preset time. Meanwhile, the convergence speed can be adjusted through the parameter design. Finally, it is proved that the control algorithm ensures that all signals in the closed-loop systems are semi-globally uniformly ultimately bounded. The effectiveness of the algorithm is verified by a numerical simulation.