This paper is concerned with the distributed H∞ filtering problem over sensor networks subject to time varying transmission delays. First, the classical Round-Robin protocol is used for the scheduling of samplers' information towards the corresponding filter. Second, a distributed event-triggering transmission scheme is introduced for information communication among distributed filters. As a result, communication and energy resources can be saved significantly while certain system performance can be preserved. Third, the resulting filtering error system is modeled as a switched system with time-varying delays. By employing Lyapunov-Krasovskii functional approach, a linear matrix inequality (LMI)-based sufficient condition is established which guarantees the filtering error system asymptotically stable with prescribed H∞ performance. An algorithm for both the distributed filters and event-triggering parameters is presented on the basis of solutions of a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.