Lightweight　aggregate　concrete　(LWAC)　is　a　superior　material　due　to　its　light　weight　and　high　strength.　There　however　remain　significant　lacunae　in　engineering　knowledge　with　regards　to　shear　failure　of　LWAC　beams.　Focusing　on　exploring　the　shear　resistance　and　the　corresponding　size　effect　in　shear　failure　of　LWAC　beams　wrapped　with　CFRP　sheets,　we　propose　a　3D　meso-scale　simulation　method　to　evaluate　the　structural　behavior　of　both　LAWC　and　NWC　(normal　weight　concrete)　beams　wrapped　with　CFRP　sheets.　The　concrete　material　is　viewed　as　a　complex　heterogeneous　material　consisting　of　mortar　matrix　in　which　are　dispersed　various　aggregates　with　interface　transition　zone　between　them.　It　is　hypothesized　here　the　CFRP　and　the　concrete　beams　are　perfectly　bonded　and　we　investigate　the　effects　of　structural　size,　of　CFRP　ratio　and　of　aggregate　type　on　the　shear　failure　of　a　CFRP-strengthened　concrete　beam.　Besides,　we　analyze　also　the　shear　contribution　by　CFRP　on　the　LWAC　beams　having　different　structural　sizes　(i.e.　beam-depth)　and　the　size　effect　on　the　nominal　shear　strength　of　CFRP-strengthened　LWAC　beams.　Based　on　the　numerical　results　via　3D　mesoscale　simulation,　we　propose　a　novel　size　effect　law　that　can　quantitatively　describe　the　influence　of　CFRP　fiber　ratio　on　shear　strength　of　the　CFRP-strengthened　concrete　beam,　and　the　newly　proposed　law　is　verified　by　experimental　data　and　simulation　results.