In　the　existing　methods　for　differentially　private　histogram　publication,　a　histogram　is　mapped　to　a　perfect　m-ary　range　tree.　The　accuracies　of　queries　are　boosted　through　consistency　constraints　of　the　queries.　However,　not　all　histograms　in　real　application　can　be　mapped　to　perfect　m-ary　range　trees　directly.　In　this　paper,　a　range　tree　structure,　k-range　tree,　is　firstly　put　forward.　By　k-range　tree,　an　arbitrary　histogram　is　mapped　to　a　range　tree.　Secondly,　the　theoretical　analysis　shows　that　for　differentially　private　histogram　publication　for　arbitrary　range　tree　structure,　the　error　of　range　counting　queries　still　can　be　further　reduced　by　solving　the　best　linear　unbiased　estimation　of　the　tree　node　values　through　consistency.　Finally,　a　differentially　private　histogram　publication　algorithm　based　on　local　best　linear　unbiased　estimation(LBLUE)　for　arbitrary　range　tree　structure　is　proposed.　Experiment　is　carried　out　to　compare　LBLUE　and　the　traditional　algorithms　on　the　accuracy　of　range　counting　queries　in　the　released　histogram　and　the　algorithm　efficiency.　Experimental　results　show　that　LBLUE　is　effective　and　feasible.　©　2015,　Science　Press.　All　right　reserved.