This paper investigates the adaptive state-feedback stabilization problem for a class of high-order stochastic non-linear systems with unknown lower and supper bounds for uncertain control coefficients. Under some weaker and reasonable assumptions, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution on [0,infinity), the equilibrium of interest is globally stable in probability and the states can be regulated to the origin almost surely. A simulation example is given to show the systematic design and effectiveness of the controller.