This article studies the distributed adaptive event-triggered consensus control problem of linear multiagent systems. A strong non-Zeno mixed adaptive dynamic event-triggering scheme is proposed, which guarantees a strictly positive minimum interevent time (MIET) between any two consecutive events. A model-based event-triggered fully distributed adaptive control law is presented without using prior global information about the communication topology. Moreover, a hybrid system model is constructed to facilitate the stability analysis of the closed-loop system. It is shown that the proposed control strategy can achieve asymptotic consensus of all agents via intermittent communication in a fully distributed way, while guaranteeing the strictly positive MIET property. Finally, the effectiveness of the designed control method is illustrated by a simulation example.