This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.