In this paper, the variance-constrained H∞ filtering problem is investigated for a class of discrete-time stochastic parameter systems. An event-triggered communication protocol is adopted in order to reduce the communication burden where the measurement information required by the filter is updated only when a certain prescribed event is triggered. The purpose of the addressed filtering problem is to design a recursive filter such that, in the presence of random parameter perturbations and external noise disturbances, both the prespecified H∞ performance index and the variance constraints on the filtering errors are satisfied over a finite-horizon. Intensive stochastic analysis is carried out and recursive matrix inequality technique is developed to obtain the filter parameters. Such a filter design scheme is based on the solution to a set of forward recursive matrix inequalities and therefore facilitates the on-line implementation. Finally, the usefulness of the developed event-triggered recursive filter design scheme is demonstrated by a numerical simulation example.