For　k≥　2　,　let　H　be　a　k-uniform　connected　hypergraph　on　n　vertices　and　m　edges.　The　transversal　number　τ(H)　is　the　minimum　number　of　vertices　that　intersect　every　edge.　We　prove　the　following　inequality:　τ(H)≤(k-1)m+1k.　Furthermore,　we　characterize　the　extremal　hypergraphs　with　equality　holds.　Based　on　the　proofs,　some　combinatorial　algorithms　on　the　transversal　number　are　designed.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.