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A class of minimum-phase stochastic nonlinear systems with model uncertainty was dealt with. In order to obtain an output feedback control which can make the response of a closed-loop system attenuate noise, and when noise does not exist, the closed-loop system will be stochastically asymptotically stable. First, an assumption was made, in which the a subsystem in the model system was stochastic input state stable, and the drift and diffusion components in the system both depended on the state of the subsystem and output. Then, a reduced-order observer was designed to get a new equivalent system. Next, by means of back-stepping the output feedback control for the new equivalent system was obtained. Finally, the closed-loop system globally stochastic asymptotically stable in probability within the absence of disturbance, and disturbance attenuation was made as well.