Abstract: Consensus problem was studied for continuous-time linear high-order multi-agent system with time-varying delay under multi-type switching communication topologies under the case that the system switches between consensusable and unconsensusable communication topologies.This consensus problem was equivalently transformed into an asymptotic stability problem of a corresponding switched delay system by a linear transformation.Based on the stability theory of the switched systems and time-delay systems,a sufficient condition was presented by the average dwell-time method in terms of linear matrix inequalities(LMIs) to guarantee the consensus of the multi-agent system.The simulation result illustrates the effectiveness of the obtained results.