In　this　paper,　we　propose　a　novel　quantum　network　coding　scheme　to　achieve　the　perfect　transmission　of　quantum　states　without　loss　of　information.　In　our　scheme,　two　pairs　of　non-maximally　entangled　states　are　pre-shared　between　senders.　By　applying　the　local　operations　at　the　sender,　the　perfect　transmission　of　quantum　states　can　be　achieved　on　the　butterfly　network.　Firstly,　by　adding　auxiliary　particles　to　the　senders　on　the　butterfly　network,　the　senders　can　judge　whether　the　quantum　state　transmission　can　be　achieved　or　not　in　advance.　The　outstanding　advantage　of　our　scheme　is　that　the　transmission　results　of　quantum　states　on　the　butterfly　network　can　be　predicted　in　advance.　When　the　transmission　fails,　the　quantum　state　will　not　be　lost.　The　sender　does　not　need　to　re-prepare　the　quantum　state　for　retransmission.　Secondly,　in　the　proposed　scheme,　not　only　the　resources　of　quantum　channel　and　classical　channel　are　greatly　saved,　but　also　only　two-bit　information　is　send　through　classical　channel　at　the　bottleneck.　Thirdly,　our　scheme　avoids　preparing　Bell　basis　to　measure　two-particle　states　and　uses　Z-basis　and　X-basis　to　measure　single-particle　states,　which　will　make　the　experimental　realization　simplified.　Finally,　we　also　extend　the　scheme　to　the　k-pair　quantum　network　and　give　an　example　of　quantum　3-pair　network　communication.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC　part　of　Springer　Nature.