In　this　paper,　protocols　of　quantum　private　comparison　of　equality　(QPCE)　are　investigated.　We　study　the　security　of　previous　QPCE　protocols　with　a　semi-honest　third　party　(TP)　from　the　viewpoint　of　secure　multiparty　computation　and　show　that　QPCE　protocol　(Chen　et　al.　Quantum　Inf　Process　2012)　has　an　obvious　security　flaw.　A　vicious　inside　attacker　impersonating　TP　or　the　compromised　TP　colluding　with　a　dishonest　inside　player　can　steal　other　player＇s　secret　successfully.　An　improved　efficient　and　feasible　QPCE　protocol　is　proposed.　In　our　improved　scheme,　only　the　two　players　can　deduce　the　results　of　comparisons　based　on　their　shared　key,　and　others　will　learn　no　information　of　the　comparison　results,　even　the　length　of　secrets.　The　cost　of　communication　is　also　be　optimized.　Our　scheme　can　resist　various　kinds　of　attacks　from　both　the　outside　eavesdroppers　and　the　inside　players,　even　the　TP.