The　consensus　problem　is　investigated　for　high-order　continuous-time　linear　multi-agent　systems　with　timevarying　delay　protocol　over　switching　directed　communication　topologies.　By　using　a　linear　transformation,　the　consensus　problem　is　equivalently　transformed　into　the　asymptotic　stability　problem　of　a　corresponding　switched　delay　system.　Under　the　assumption　that　each　of　the　communication　topologies　is　consensusable,　with　the　help　of　the　scheme　of　average　dwelltime　in　switched　systems,　a　sufficient　condition　is　presented　in　terms　of　linear　matrix　inequalities(LMIs)　to　guarantee　the　consensus　of　the　agents.　Simulation　result　shows　the　effectiveness　of　the　obtained　results.　©　2016,　Editorial　Office　of　Control　and　Decision.　All　right　reserved.