Dear Editor, This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes. The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics. Toward this aim, a hybrid impulsive controller, featuring both delayed and non-delayed impulses, is developed. Sufficient conditions of mean square exponential stability of the delayed stochastic synchronization error system are then derived. It is further shown that exponential synchronization can still be preserved even if the impulsive controller involves only delayed impulses. An illustrative example is finally presented to demonstrate the effectiveness of the obtained theoretical results.