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Leader-following consensus of multi-agent systems with general linear models is investigated via event-based impulsive control approach. Event-based impulsive controller and state-dependent triggering function are designed. Impulsive instants are determined by certain triggering events, that is, impulsive effect performs only at the instants when events occur, and so as controller update. Sufficient conditions on leader-following consensus are proposed by using stability theory of impulsive differential equations, matrix theory, and inequality technique. Zeno-behavior is also excluded for the concerned closed-loop system. Besides, a technique that used the state information of agents only at event instants is proposed to avoid continuous communication among agents. Finally, an example is presented to illustrate the effectiveness of the obtained theoretical results.