This　paper　investigates　the　event-triggered　consensus　control　problem　for　multi-agent　systems　with　Markov　switching　topologies.　By　a　linear　transformation　method,　the　mean-square　consensus　problem　under　event-triggered　protocol　is　transformed　into　the　mean-square　stability　problem　subject　to　a　certain　constraint　condition.　Then　by　constructing　Lyapunov　function　and　employing　the　weak　infinitesimal　operator,　the　mode-dependent　consensus　controller　gains　are　designed　in　terms　of　a　bilinear　matrix　inequality.　In　order　to　write　bilinear　matrix　inequality　as　a　set　of　linear　matrix　inequalities,　three　kinds　of　iterative　algorithms　are　developed.　Finally,　a　simulation　example　is　provided　to　verify　the　validity　of　the　presented　algorithms.　©　2021　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.