In　recent　years,　differential　privacy　data　publishing　has　received　considerable　attention.　However,　existing　techniques　on　achieving　differential　privacy　for　answering　range-count　queries　fail　to　release　data　with　high　quality.　In　this　paper,　we　propose　a　new　solution　for　answering　range-count　queries　under　the　framework　of　Ε-differential　privacy,　which　aims　to　maintain　high　data　utility　while　protecting　individual　privacy.　The　key　idea　of　the　proposed　solution　is　to　add　noise　on　an　average　tree,　in　which　each　node　value　is　the　average　value　of　all　its　leaf　nodes.　Experimental　analysis　is　designed　by　comparing　the　proposed　solution　and　the　classic　algorithms　on　the　released　data　utility.　The　theoretical　analysis　and　experimental　results　show　that　our　solution　is　effective　and　feasible.　©　2012　Springer-Verlag.