The　purpose　of　the　research　is　to　investigate　the　influence　of　strain　rate　and　shear-span　ratio　on　the　shear　strength　and　size　effect　of　Basalt　Fiber　Reinforced　Plastics　(BFRP)　reinforced　concrete　beams　without　stirrups,　and　then　to　establish　the　theoretical　formula　quantitatively　describing　the　size　effect.　A　three-dimensional　meso-scale　numerical　model　of　BFRP　reinforced　concrete　beams　was　established　to　simulate　the　shear　failure　of　geometrically　similar　specimens.　Finally,　a　new　size　effect　law　was　established　to　predict　the　shear　capacity　of　BFRP　reinforced　concrete　beams　with　different　structural　sizes　under　dynamic　loadings.　The　results　indicate　that:　1)　the　shear　capacity　of　BFRP　reinforced　concrete　beams　increases　with　the　increase　of　strain　rate,　while　the　size　effect　in　shear　failure　of　BFRP　reinforced　concrete　beams　is　weakened　simultaneously;　2)　the　increase　of　shear-span　ratio　weakens　the　strain-rate　effect,　but　has　an　ignorable　influence　on　the　size　effect;　3)　the　new　size　effect　law　can　be　used　to　quantitatively　describe　the　effect　of　strain　rate　on　size　effect　and　is　in　good　agreement　with　the　existing　experiments.　©　2021　Elsevier　Ltd