The　aggregate　size　plays　an　important　role　in　the　nonlinear　mechanical　behaviour　of　concrete,　which　is　strongly　related　to　the　size　effect.　In　this　study,　the　meso-mechanical　modelling　method　has　been　established　based　on　the　continuous　grading　aggregate　model　to　simulate　the　uniaxial　compressive　failure　behaviour　under　quasi-static　load　of　concrete　square　samples　having　different　side　lengths,　maximum　aggregate　sizes　(MAS)　and　concrete　strength　grades.　The　numerical　results　demonstrated　that　the　MAS　affected　the　crack　propagation　form　in　the　internal　components　of　concrete　and　the　nominal　compressive　strength　decreased　with　the　increasing　MAS;　the　increasing　MAS　could　enhance　the　sensitivity　of　strength-to-structural　size　and　make　the　size　effect　more　obvious.　In　addition　to　the　numerical　analysis,　a　modified　Type-2　size　effect　law　considering　the　MAS　for　the　nominal　compressive　strength　has　been　proposed　from　theoretical　perspective,　which　makes　it　possible　to　quantitatively　predict　the　size　effect　behaviour　of　compressive　strength.　Mesoscopic　simulation　results　and　some　experimental　results　have　validated　the　modified　Type-2　size　effect　law.