Many　concrete　engineering　structures　have　already　withstood　the　historical　loads　(such　as　initial　compressive/　tensile　load)　prior　to　being　subjected　to　dynamic　loads.　The　historical　load　and　structure　size　are　two　influential　factors　on　dynamic　mechanical　performance　of　concrete.　Exploring　the　dynamic　size　effect　of　concrete　with　different　loading　histories　is　a　valuable　task.　In　this　work,　the　influence　of　pre-static　compressive/tensile　loads　on　dynamic　compressive　failure　and　the　corresponding　dynamic　size　effect　was　investigated　by　the　developed　mesoscale　finite　element　method.　The　research　results　show　that　the　dynamic　compressive　strength　of　concrete　decreases　with　the　increasing　pre-static　compressive　load　under　low　strain-rates　while　it　increases　with　the　increasing　pre-static　tensile　load.　Dynamic　strength　under　high　strain-rates　is　not　affected　by　the　pre-static　loads.　Moreover,　as　the　concrete　has　withstood　more　pre-static　loads,　the　dynamic　size　effect　on　compressive　strength　becomes　more　obvious　under　low　strain-rates.　Finally,　the　numerical　results　were　analyzed　and　confirmed　by　the　application　of　Weibull　size　effect　law.