Fork　＞=　2,　let　H　be　a　k-uniform　connected　hypergraph　on　n　vertices　and　m　edges.　The　transversal　number　tau　(H)　is　the　minimum　number　of　vertices　that　intersect　every　edge.　We　prove　the　following　inequality:　tau　(H)　＜=　(k-1)m+1　/k.　Furthermore,　we　characterize　the　extremal　hypergraphs　with　equality　holds.　Based　on　the　proofs,　some　combinatorial　algorithms　on　the　transversal　number　are　designed.