This research deals with the stabilization of the stochastic nonlinear systems. In order to achieve the asymptotic stability in probability with respect to unknown bounded disturbances, a control Lyapunov function is applied to present a modified Sontag's homogeneous controller. The obtained results reveal that the presented control achieves the desirable robust asymptotic stability in probability. The finite-time stability in probability for stochastic nonlinear systems is also discussed in this manuscript. Simulation examples are provided to demonstrate the effectiveness of the controllers.