This paper is concerned with the problem of event-triggered H∞ control for a class of networked control systems with nonlinear perturbations. The nonlinear perturbations appear in both the system dynamic equation and the controlled output signals. An event-triggered transmission scheme is introduced to select `necessary' sampled-data packets to be transmitted through a communication network. Under the event-triggered transmission scheme, the closed-loop system is modeled as a system with an interval time-varying delay. Employing the matrix-based quadratic convex approach recently reported in the literature, a novel sufficient condition on the existence of desired event-triggered H∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.