Stochastic noise is unavoidable in the implementation of real complex artificial neural network model and large scale integrated circuit. Therefore, the practical research significance of stochastic memristor-based neural network is important. Aiming at the problem of synchronization control of stochastic memristor-based neural networks with time-varying delays, based on non-smooth analysis and the theory of set-valued maps and stochastic differential inclusions, a novel control method is given using the method of Lyapunov functional and the fundamental inequality. State feedback controller has been put forward to achieve synchronization index for the drive system and corresponding response system of the stochastic memristor-based neural network. Meanwhile, a numerical example is given to verify the theoretical analysis in this paper.