Great　progresses　have　been　made　in　static　size　effect　of　concrete,　while　almost　no　efforts　have　been　conducted　in　dynamic　size　effect　of　concrete.　The　macro　nonlinearity　and　size　effect　of　concrete　should　be　attributed　to　the　inner　heterogeneities.　Herein,　a　meso-scale　simulation　method　was　built　to　study　the　dynamic　failure　and　size　effect　of　concrete.　In　the　approach,　the　concrete　heterogeneities　were　explicitly　described,　and　the　strain　rate　effect　for　the　meso　components　were　also　taken　into　account.　Taking　squared　concrete　specimens　as　examples,　the　dynamic　compressive　failure　and　the　size　effect　of　concrete　under　different　strain　rates　from　10(-5)/s　to　200/s　were　modelled　and　investigated.　The　effect　of　strain　rate　on　the　size　effect　in　compressive　strength　of　concrete　was　also　explored.　The　simulation　results　indicate　that,　there　exists　a　critical　strain　rate　((epsilon)　over　dot(cr)　=　1/s).　When　the　applied　strain　rate　is　less　than　the　critical　strain　rate,　the　compressive　strength　decreases　with　increasing　the　specimen　size　and　the　size　effect　on　the　dynamic　compressive　strength　is　weakened　as　the　strain　rate　increases.　The　dynamic　compressive　strength　turns　to　be　independent　on　the　structural　size　of　the　specimen　for　the　critical　strain　rate.　When　the　applied　strain　rate　is　more　than　the　critical　strain　rate,　the　compressive　strength　increases　with　the　increase　of　specimen　size　and　the　size　effect　on　the　dynamic　compressive　strength　is　enhanced　as　the　strain　rate　increases.　Finally,　based　on　the　influencing　mechanism　of　strain　rate　effect　to　dynamic　strength　and　size　effect,　a　Static　and　Dynamic　unified　Size　Effect　Law　(i.e.　SD-SEL)　for　compressive　strength　of　concrete　was　established.　The　proposed　size　effect　law　was　also　calibrated　by　the　meso-scale　simulation　results.