This article takes a fast finite-time control of stochastic nonlinear systems into account. The presence of unknown stochastic disturbance terms makes the traditional fast finite-time control approaches unavailable. To deal with this difficulty, by establishing an auxiliary function and using Jensen's inequality, in Lemma 6, a new criterion of fast finite-time stability is first established for the uncertain stochastic system. Based on the approximation ability of neural networks (NNs), an innovative fast finite-time strategy is put forward for stochastic nonlinear systems. Furthermore, by adopting the presented fast finite-time stability criterion, the stability of the stochastic systems is confirmed. Finally, two simulations are implemented to validate the feasibility of the presented NN control strategy.