The　aim　of　this　paper　is　to　study　how　to　solve　a　type　of　matrix　game　with　interval　payoffs.　In　this　paper,　the　interval　inequality　relations　and　the　concept　of　solutions　of　the　matrix　game　with　interval　payoffs　are　defined.　Based　on　the　fuzzy　ranking　index　defined,　the　solution　of　the　matrix　game　with　interval　payoffs　can　be　obtained　through　solving　a　pair　of　bi-objective　linear　programming　models　derived　from　the　constructed　auxiliary　interval　programming　models.　It　is　shown　that　the　models　proposed　in　this　paper　extend　those　of　the　classical　matrix　game.　The　validity　and　applicability　of　the　proposed　methodology　are　illustrated　with　a　numerical　example.