Existing　protocols　for　private　database　queries　in　the　quantum　context　are　classified　into　two-dimensional　protocols　and　D-dimensional　ones.　For　the　two-dimensional　protocols,　to　obtain　a　meaningful　n-bit　message　from　the　database,　the　user　Alice　has　to　query　n　times　to　get　all　the　n　bits.　However,　each　query　may　leak　Alice＇s　privacy　once　the　server　Bob　obtains　the　address　she　queried,　since　each　queried　bit　contributes　to　the　whole　queried　message.　Apparently,　the　longer　the　queried　message　is,　the　worse　the　user　privacy　becomes.　By　contrast,　the　D-dimensional　protocol　allows　the　user　to　query　a　multi-bit　block　with　length　no　more　than　logd　from　the　database　via　only　one　query.　In　this　paper,　we　propose　a　novel　D-dimensional　quantum　protocol　for　private　database　query.　In　contrast　to　existing　D-dimensional　protocols,　the　proposed　protocol　allows　the　user　to　retrieve　a　message　of　theoretically　arbitrary　length　without　the　limitation　of　the　dimension　d　by　using　a　subtle　classical　post-processing　strategy.　Furthermore,　the　server＇s　outcomes　of　measurement　can　be　irrelevant　for　the　implementation　of　the　protocol　thus　relaxing　his/her　quantum　ability.　Finally,　the　security　of　the　proposed　protocol　in　the　zero-error　case　has　been　proved　in　terms　of　the　user　privacy　and　database　security.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.