In　order　to　reduce　the　communication　cost,　a　non-interactive　quantum　deniable　authentication　based　on　asymmetric　quantum　cryptography　is　proposed.　In　the　new　scheme,　the　sender　and　receiver　without　interaction　first　agree　a　sharing　secret　key　by　utilizing　their　public　and　private　key　and　then　the　sender　generates　the　authentication　information　according　to　the　sharing　secret　key,　similarly,　the　receiver　can　also　generate　the　same　authentication　codes　according　to　the　sharing　secret　key.　So　the　receiver　cannot　prove　the　source　of　the　message　to　a　third　party　but　can　identify　the　true　source　of　a　given　message.　Compared　with　our　previous　schemes　based　on　interaction,　this　new　scheme　has　the　remarkable　advantages　of　reducing　the　communication　cost,　lessening　the　difficulty　and　intensity　of　necessary　operations,　and　without　help　of　a　trusted　center.　Finally,　the　security　analysis　results　show　that　this　new　scheme　also　satisfies　the　same　basic　security　requirements　of　deniable　authentication　protocol　such　as　completeness,　deniability,　and　can　withstand　forgery　attack,　impersonation　attack　and　inter-resend　attack.　(C)　2016　Elsevier　GmbH.　All　rights　reserved.