The　static　size　effect　of　concretes　has　been　relatively　well　addressed,　while　studies　on　the　dynamic　size　effect　of　concretes　have　not　yet　generated　a　unified　understanding.　The　size　effect　of　concrete　can　be　attributed　to　the　inner　heterogeneities.　Herein　the　study,　a　meso-scale　simulation　method　was　built　to　study　the　dynamic　failure　and　size　effect　of　concrete.　Considering　the　material　heterogeneity　and　strain　rate　effects　of　meso-components,　concrete　was　simulated　as　a　three-phase　composite　composed　of　aggregate,　mortar　matrix　and　interface　transition　zone　at　meso-scale.　The　square　concrete　specimens　with　different　sizes　were　built　and　the　dynamic　compressive　failure　and　the　size　effect　of　concrete　under　the　strain　rates　from　10-5s-1　to　200s-1　were　investigated　using　the　meso-scale　simulation　method.　There　are　obvious　differences　between　static　size　effect　and　dynamic　size　effect　in　the　compressive　strength　of　concrete.　There　exists　a　critical　strain　rate　(the　critical　strain　rate　is　s-1　approximately).　When　the　applied　strain　rate　is　less　than　the　critical　strain　rate,　the　size　effect　on　the　dynamic　compressive　strength　is　weakened　or　suppressed　as　the　strain　rate　increases.　The　dynamic　compressive　strength　would　be　independent　of　the　structural　size　of　the　specimen　when　the　applied　strain　rate　reaches　the　critical　strain　rate.　When　the　applied　strain　rate　is　more　than　the　critical　strain　rate,　the　size　effect　on　the　dynamic　compressive　strength　is　strengthened　as　the　strain　rate　increases.　Finally,　based　on　the　simulation　results,　the　mechanism　of　concrete　dynamic　size　effect　was　analyzed　and　discussed.　©　2019,　Engineering　Mechanics　Press.　All　right　reserved.