The　aim　of　this　paper　is　to　develop　an　effective　method　for　solving　matrix　games　with　payoffs　of　triangular　fuzzy　numbers　(TFNs)　which　are　arbitrary.　In　this　method,　it　always　assures　that　players＇　gain-floor　and　loss-ceiling　have　a　common　TFN-type　fuzzy　value　and　hereby　any　matrix　game　with　payoffs　of　TFNs　has　a　TFN-type　fuzzy　value.　Based　on　duality　theorem　of　linear　programming　(LP)　and　the　representation　theorem　for　fuzzy　sets,　the　mean　and　the　lower　and　upper　limits　of　the　TFN-type　fuzzy　value　are　easily　computed　through　solving　the　derived　LP　models　with　data　taken　from　1-cut　set　and　0-cut　set　of　fuzzy　payoffs.　Hereby　the　TFN-type　fuzzy　value　of　any　matrix　game　with　payoffs　of　TFNs　can　be　explicitly　obtained.　Moreover,　we　can　easily　compute　the　upper　and　lower　bounds　of　any　Alfa-cut　set　of　the　TFN-type　fuzzy　value　for　any　matrix　game　with　payoffs　of　TFNs　and　players＇　optimal　mixed　strategies　through　solving　the　derived　LP　models　at　any　specified　confidence　level　Alfa.　The　proposed　method　in　this　paper　is　demonstrated　with　a　numerical　example　and　compared　with　other　methods　to　show　the　validity,　applicability　and　superiority.　©　2012　Elsevier　B.V.　All　rights　reserved.