Let　and　be　fixed　integers,　and　let　H　be　an　r-uniform　hypergraph　with　n　vertices　and　m　edges.　In　1997,　Bollobas　and　Scott　conjectured　that　H　has　a　vertex-partition　into　k　sets　with　at　most　edges　in　each　set.　So　far,　this　conjecture　was　confirmed　when　or　.　In　this　paper,　we　show　that　it　holds　for　for　any　.