This paper investigates the output consensus problem for heterogeneous linear multi-agent systems via event-triggered control. By introducing a dynamic compensator for each agent. a fully distributed event-triggered control strategy with an adaptive event-triggering mechanism is proposed. It is shown that under the proposed control strategy, all agents asymptotically achieve output consensus with intermittent communication in a fully distributed manner. Moreover, with the proposed event-triggering mechanism. Zeno behavior is strictly excluded for each agent. Compared with existing mechanisms, the proposed event-triggering mechanism is independent of any global information and avoids the continuous monitoring issue. Finally, a numerical example is provided to illustrate the effectiveness of the proposed event-triggered control strategy.