Constrained　matrix　games　with　payoffs　of　triangular　fuzzy　numbers　(TFNs)　are　a　type　of　matrix　games　with　payoffs　expressed　by　TFNs　and　sets　of　players＇　strategies　which　are　constrained.　So　far　as　we　know,　no　study　have　yet　been　attempted　for　constrained　matrix　games　with　payoffs　of　TFNs　since　there　is　no　effective　way　to　simultaneously　incorporate　the　payoffs＇　fuzziness　and　strategies＇　constraints　into　classical　and/or　fuzzy　matrix　game　methods.　The　aim　of　this　paper　is　to　develop　an　effective　methodology　for　solving　constrained　matrix　games　with　payoffs　of　TFNs.　In　this　methodology,　we　introduce　the　concepts　of　Alpha-constrained　matrix　games　for　constrained　matrix　games　with　payoffs　of　TFNs　and　the　values.　By　the　duality　theorem　of　linear　programming,　it　is　proven　that　players＇　gain-Floor　and　loss-ceiling　always　have　a　common　interval-type　value　and　hereby　any　Alpha-constrained　matrix　game　has　an　interval-type　value.　Moreover,　using　the　representation　theorem　for　the　fuzzy　set,　it　is　proven　that　any　constrained　matrix　game　with　payoffs　of　TFNs　always　has　a　TFN-type　fuzzy　value.　The　auxiliary　linear　programming　models　are　derived　to　compute　the　lower　and　upper　bounds　of　the　interval-type　value　and　optimal　strategies　of　players　for　any　Alpha-constrained　matrix　game.　In　particular,　the　mean　and　the　lower　and　upper　limits　of　the　TFN-type　fuzzy　value　of　any　constrained　matrix　game　with　payoffs　of　TFNs　can　be　directly　obtained　through　solving　the　derived　three　linear　programming　models　with　data　taken　from　only　1-cut　and　0-cut　of　payoffs.　Hereby　the　TFN-type　fuzzy　value　of　any　constrained　matrix　game　with　payoffs　of　TFNs　are　easily　computed.　The　proposed　method　in　this　paper　is　compared　with　other　methods　and　its　validity　and　applicability　are　illustrated　with　a　numerical　example.　(c)　2011　Elsevier　Ltd.　All　rights　reserved.