Matrix　game　theory　is　concerned　with　how　two　players　make　decisions　when　they　are　faced　with　known　exact　payoffs.　The　aim　of　this　paper　is　to　develop　a　simple　and　an　effective　linear　programming　method　for　solving　matrix　games　in　which　the　payoffs　are　expressed　with　intervals.　Because　the　payoffs　of　the　matrix　game　are　intervals,　the　value　of　the　matrix　game　is　an　interval　as　well.　Based　on　the　definition　of　the　value　for　matrix　games,　the　value　of　the　matrix　game　may　be　regarded　as　a　function　of　values　in　the　payoff　intervals,　which　is　proven　to　be　non-decreasing.　A　pair　of　auxiliary　linear　programming　models　is　formulated　to　obtain　the　upper　bound　and　the　lower　bound　of　the　value　of　the　interval-valued　matrix　game　by　using　the　upper　bounds　and　the　lower　bounds　of　the　payoff　intervals,　respectively.　By　the　duality　theorem　of　linear　programming,　it　is　proven　that　two　players　have　the　identical　interval-type　value　of　the　interval-valued　matrix　game.　Also　it　is　proven　that　the　linear　programming　models　and　method　proposed　in　this　paper　extend　those　of　the　classical　matrix　games.　The　linear　programming　method　proposed　in　this　paper　is　demonstrated　with　a　real　investment　decision　example　and　compared　with　other　similar　methods　to　show　the　validity,　applicability　and　superiority.　©　2011　Elsevier　Ltd.