The problem of passivity analysis of stochastic neural networks with leakage delay and Markovian jumping parameters is considered in this article. By utilizing the Lyapunov functional method, the Ito differential rule and matrix analysis techniques, we establish sufficient criterion such that the stochastic neural networks is passive in the sense of expectation. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results. (C) 2016 Elsevier B.V. All rights reserved.