This paper investigates asymptotic stabilization for linear systems over networks based on event-driven communication. A new communication logic is proposed to reduce the feedback effort, which has some advantages over traditional ones with continuous feedback. Considering the effect of time-varying transmission delays, the criteria for the design of both the feedback gain and the event-triggering mechanism are derived to guarantee the stability and performance requirements. Finally, the proposed techniques are illustrated by an inverted pendulum system and a numerical example.