This paper investigates a finite-time tracking control of stochastic nonlinear systems with actuator failures. As the nonlinearities and actuator failures are completely unknown, the existing control methods are unavailable. By applying an approximation property of fuzzy logic systems, an adaptive finite-time control strategy is presented. Since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error, Lemma 5 is first established. Under the proposed scheme, the actuator failures are compensated successfully, and the finite-time tracking performance and stability of stochastic nonlinear system are assured. Based on Lemma 5 and Jessen's inequality, the finite-time stability of stochastic nonlinear systems is proved.