The　purpose　of　this　paper　is　to　develop　an　effective　methodology　for　solving　constrained　matrix　games　with　payoffs　of　trapezoidal　fuzzy　numbers　(TrFNs),　which　are　a　type　of　two-person　non-cooperative　games　with　payoffs　expressed　by　TrFNs　and　players＇　strategies　being　constrained.　In　this　methodology,　it　is　proven　that　any　Alfa-constrained　matrix　game　has　an　interval-type　value　and　hereby　any　constrained　matrix　game　with　payoffs　of　TrFNs　has　a　TrFN-type　value.　The　auxiliary　linear　programming　models　are　derived　to　compute　the　interval-type　value　of　any　Alfa-constrained　matrix　game　and　players＇　optimal　strategies.　Thereby　the　TrFN-type　value　of　any　constrained　matrix　game　with　payoffs　of　TrFNs　can　be　directly　obtained　through　solving　the　derived　four　linear　programming　models　with　data　taken　from　only　1-cut　and　0-cut　of　TrFN-type　payoffs.　Validity　and　applicability　of　the　models　and　method　proposed　in　this　paper　are　demonstrated　with　a　numerical　example　of　the　market　share　game　problem.　©　2012　Springer　Science+Business　Media　New　York.