In this paper, an output consensus problem for a heterogeneous linear multiagent system with a predictive event-triggered mechanism on directed graphs is investigated. An event-triggered consensus protocol is proposed by introducing an internal reference model for each agent to handle the heterogeneity existing in the system. With the proposed mechanism, each agent predicts its internal reference model's input by employing the estimate of the internal reference model's state differences between itself and its neighbor agents. As it considers the internal reference model's inputs of agents, the system requires far fewer event-triggered times to achieve consensus, leading to a significant reduction in communication cost among agents. A necessary and sufficient condition of the output consensus for the heterogeneous linear multiagent system is put forth. Furthermore, Zeno behavior can be ruled out for each agent. Some numerical examples are given to demonstrate the effectiveness of the proposed control mechanism.