The　size　effect　and　macroscopic　nonlinearity　of　concrete　are　caused　by　its　inherent　heterogeneity.　Considering　the　mesoscopic　heterogeneity,　concrete　was　regarded　as　a　tril-phase　composite　material　consisting　of　aggregate,　mortar　matrix　and　the　interfacial　transition　zone　(ITZ)　at　meso-scale.　Numerical　concrete　specimens　sized　by　150　mm×150　mm,　300　mm×300　mm　and　600　mm×600　mm　were　set　up.　First,　several　uniaxial　compressive　tests　of　square　concrete　specimens　were　conducted　and　the　mechanical　parameters　of　the　ITZs　were　fixed　by　an　inversion　method.　Then　the　failure　behavior　and　the　size　effect　of　concrete　under　biaxial　compression　were　analyzed.　Some　conclusions　can　be　drawn　as,　1)　damage　failure　evolves　with　dimension　of　the　specimen,　and　difference　of　the　fracture　energy　dissipated　per　unit　is　the　main　reason　of　the　presence　of　size　effect　in　concrete　subjected　to　bi-axial　compression.　2)　an　obvious　size　effect　can　be　observed　on　the　uniaxial/biaxial　compressive　strength　of　concrete　and　the　simulation　results　of　present　work　follow　closely　the　size　effect　law　(SEL)　proposed　by　Bažant.　©　2017,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.