This paper is concerned with leader-following consensus of general linear multi-agent systems. First, to save the limited communication resources, a novel distributed event-triggered control strategy with state-dependent and time-dependent thresholds is delicately developed. Without requiring continuous communication among the following agents, the proposed strategy can allow for larger minimum inter-event times. Then, by employing the Lyapunov function method, bounded consensus for multi-agent systems is achieved. Moreover, it is proved that the triggering time sequence does not exhibit Zeno behavior. Finally, the effectiveness of the control mechanism is verified by a numerical example.