This article contributes to design an event-triggered H-infinity controller for networked control systems with network channel delay. First, the network channel delay is modeled as a distributed delay with a probability density function as its kernel. Then, the closed-loop event-triggered control system is established as a distributed delay system. To make full use of the delay probability distribution, the Lyapunov-Krasovskii functional is constructed with the distributed kernel. By applying the Lyapunov method, sufficient conditions for ensuring the stability of the closed-loop system with prescribed H-infinity performance are formulated in linear matrix inequalities. A numerical example shows that the proposed method is less conservative than some existing results considering delay distribution.