This paper investigates the time-varying formation problem for general linear multi-agent systems using distributed event-triggered control strategy. Different from the previous works, to achieve the desired time-varying formation, a dis-tributed control scheme is designed in an event-triggered way, in which for each agent the controller is triggered only at its own event times. The interaction topology among agents is assumed to be switching. The common Lyapunov function as well as Riccati inequality is applied to solve the time-varying formation problem. Moreover, the Zeno behavior of trigger-ing time sequences can be excluded for each agent. Finally, a simulation example is presented to illustrate the effectiveness of the theoretical results.