For　the　problem　of　major　solution　methods　for　matrix　games　with　fuzzy　payoffs,　an　effective　methodology　is　developed　to　solve　matrix　games　with　payoffs　expressed　by　trapezoidal　fuzzy　numbers.　In　this　methodology,　the　concept　of　α-matrix　games　is　introduced　and　players＇　fuzzy　values　are　always　identical.　The　upper　and　lower　bounds　of　any　α-cut　of　the　fuzzy　value　and　players＇　optimal　strategies　are　easily　obtained　through　solving　the　derived　four　linear　programming　problems　with　the　upper　and　lower　bounds　of　α-cuts　of　the　fuzzy　payoffs.　Particularly,　the　fuzzy　value　can　be　explicitly　estimated.　Compared　with　other　methods,　the　effectiveness　and　feasibility　of　the　proposed　method　are　illurstrated.　©,　2015,　Northeast　University.　All　right　reserved.