The　entropy　of　an　intuitionistic　fuzzy　set　(IFS)　is　a　measure　of　uncertainty　related　to　the　IFS.　The　purpose　of　this　paper　is　to　develop　a　new　axiomatical　entropy　for　an　IFS.　The　axioms　for　a　new　entropy　of　an　IFS　are　defined　and　a　mathematical　expression/formula　of　the　new　entropy　of　the　IFS　is　given.　The　newly　defined　entropy　concerns　both　the　amount　of　information　and　reliability　of　the　IFS.　It　is　proven　that　the　new　entropy　has　some　remarkable　and　useful　properties.　The　examples　and　comparison　analysis　show　the　validity　and　applicability　of　the　new　entropy　proposed　in　this　paper.