This study investigates event-triggered H_∞ filtering problem for discrete-time multi-agent systems with switching topologies. A novel distributed event-triggered control scheme is constructed to determine whether each agent should transmit the current sampled data to the filter, thus effectively save network resources. Considering the existence of network-induced delay and modeling the switching of network topologies by a Markov process, the distributed filtering error system is modeled as a closed-loop system with multiple time-varying delays by using the event-triggered control scheme and the proposed H_∞ filter. By employing Lyapunov-Krasovskii functional and linear matrix inequality method with multi-interval upper and lower bounds information, some sufficient conditions and the design method of H_∞ filter parameters are obtained to guarantee the closed-loop system to achieve asymptotic stability with an H_∞ performance index. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.