This paper investigates the event-triggered H∞ control for networked control systems under the denial-of-service (DoS) attacks. First, a novel system model is established considering random, time-constraint DoS attacks. Second, an event-triggered scheme including an off-time is proposed to reduce the unnecessary occupation of network resources, with which a prescribed minimum inter-triggering time is guaranteed and Zeno problem is avoided. Third, sufficient conditions for the existence of an event-triggered controller which ensures the exponential stability of the closed-loop system with desired H∞ performance are formulated in linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is examined by two illustrative examples, where a real communication network based on the ZigBee protocol is utilized.