This　paper　investigates　the　leader-following　consensus　problem　for　general　linear　multi-agent　systems　with　time-varying　delay.　An　observer-based　distributed　triggering　mechanism　is　proposed　to　solve　this　problem.　For　each　agent,　the　update　of　the　designed　distributed　event-triggered　controller　only　requires　the　knowledge　of　its　neighbors＇　states　at　its　own　event　time　instants.　A　sufficient　condition　is　presented　to　show　that　leader-following　consensus　of　the　multi-agent　system　can　be　reached　exponentially.　Moreover,　the　Zeno　behavior　of　the　triggering　time　sequences　is　excluded　naturally.　Finally,　the　effectiveness　of　the　proposed　control　schemes　is　illustrated　by　a　numerical　example.