This paper deals with the problem of non-fragile robust finite-time $H_{infty}$ control for a class of uncertain nonlinear stochastic It$hat{o}$ systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under state-space representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time $H_{infty}$ controller in terms of matrix inequalities. Furthermore, the problem of non-fragile robust finite-time $H_{infty}$ control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.