This paper focuses on the issue of adaptive neural output-feedback control for a class of nonlinear pure-feedback systems. A state observer is first constructed to estimate the unmeasurable state variables. Radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions and backstepping adaptive technique is utilized to construct controller. The proposed control scheme guarantees semi-globally uniformly ultimate boundedness (SGUUB) of all the signals in the closed-loop system. At last, a simulation example is used to show the effectiveness of the proposed method.