This　paper　investigates　the　consensus　problem　of　general　linear　discrete-time　multiagent　systems　by　using　distributedmodel　predictive　control　(DMPC)　with　self-triggered　mechanism.　First,　a　novel　DMPC-based　consensus　algorithm　is　proposed,　where　each　agent　only　needs　to　obtain　its　neighbors＇　predicted　state　sequences　once　at　each　time　step.　We　prove　that　the　resultant　DMPC　optimization　problem　is　feasible,　and　the　proposed　algorithm　guarantees　the　dynamic　consensus　of　agents.　Then,　to　further　reduce　the　communication　cost　and　the　energy　consumption　of　control　updates,　a　self-triggered　DMPC-based　consensus　algorithm　is　proposed　with　the　control　input　and　the　triggering　interval　jointly　optimized.　Numerical　examples　including　the　benchmark　problem　with　platooning　vehicles　are　provided　to　verify　the　effectiveness　and　advantages　of　the　proposed　algorithms.