The networked leader-following consensus for a class of multi-agent systems via an event-triggered communication scheme is investigated. By introducing a distributed event-triggered communication scheme to select the broadcast data and analyzing the effect of network-induced delays on the control input of each agent, the resulting networked multi-agent systems are modeled as an augmented system with multiple interval time-varying delays. A multiple delay bounds dependent consensus condition is obtained by a Lyapunov-Krasovskii functional approach. Based on the consensus condition of the augmented system, a consensus control protocol is designed such that all follower agents can asymptotically reach the state of the leader. The effectiveness of the proposed results is validated by a numerical example.