For the multiagent systems, how to allocate the communication resources effectively and thus prolong the life-span of the systems is an interesting problem. Event-triggered control, which can maintain an anticipated performance while reducing the communication resources of multiagent systems efficaciously, arises for solving such an issue. The majority of the obtained event-based consensus results in literature need some global information. In order to overcome the existing imperfections mentioned above, this article studies the fully distributed consensus problem of multiagent systems with general dynamics. By introducing a couple of adaptive parameters, a fully distributed leader-following consensus protocol in the event-triggered fashion is developed. In such a design, no global information is used. Moreover, the new node-based adaptive parameters developed in this paper is more efficient than traditional edge-based ones. The Zeno behavior is also proved to be excluded in the close-looped system, which makes it possible for practical applications. Finally, a simulation example is provided to demonstrate the validity of the designed strategy.