For the first time, an adaptive backstepping neural network control approach is extended to a class of stochastic nonlinear output-feedback systems. Different from the existing results, the nonlinear terms are assumed to be completely unknown and only a neural network is employed to compensate for all unknown nonlinear functions so that the controller design is more simplified. Based on stochastic LaSalle theorem, the resulted closed-loop system is proved to be globally asymptotically stable in probability. The simulation results further verify the effectiveness of the control scheme. For the first time, an adaptive backstepping neural network control approach is extended to a class of stochastic nonlinear output-feedback systems. Different from the existing results, the nonlinear terms are assumed to be completely unknown and only a neural network is employed to compensate for all unknown nonlinear functions so that the controller design is more simplified. Based on stochastic LaSalle theorem, the resulting closed-loop system is proved to be globally asymptotically stable in probability. The simulation results further verify the effectiveness of the control scheme.