The Razumikhin-type approach is introduced to solve the state feedback stabilization problem for a class of stochastic nonlinear systems with time-varying delay. Based on the Razumikhin-Mao theorem on stochastic systems and the backstepping design method, a state feedback controller is constructed to ensure the origin of closed-loop system globally asymptotically stable in probability. The limitations on the derivative of delay can be completely removed, which is the common assumption of stochastic nonlinear systems with time-varying delay. A simulation example is given to illustrate the effectiveness of the state feedback controller.