This paper is concerned with the state-feedback control for a class of stochastic high-order nonlinear systems with multiple time delays. A distinctive novelty lies in the removal of the traditional growth assumptions imposed on the delay-dependent nonlinear terms. Then, without any extra assumptions, a state-feedback controller is explicitly constructed based on the Lyapunov-Krasovskii functionals and recursive backstepping design, which guarantees the closed-loop system to be globally uniformly ultimately bounded (GUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed scheme.