supertree　is　a　connected　and　acyclic　hypergraph.　The　set　of　r-uniform　supertrees　with　n　vertices　and　the　set　of　r-uniform　supertrees　with　perfect　matchings　on　rk　vertices　are　denoted　by　Tn　and　Tr,k,　respectively.　H.　Li,　J.　Shao,　and　L.　Qi　[J.　Comb.　Optim.,　2016,　32(3):　741–764]　proved　that　the　hyperstar　Sn,r　attains　uniquely　the　maximum　spectral　radius　in　Tn.　Focusing　on　the　spectral　radius　in　Tr,k,　this　paper　will　give　the　maximum　value　in　Tr,k　and　their　corresponding　supertree.　©　2018,　Higher　Education　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.