The　bimatrix　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　bilinear　programming　method　for　solving　bimatrix　games　in　which　the　payoffs　are　represented　by　intervals.　Because　the　payoffs　of　the　bimatrix　game　are　intervals,　the　values　of　the　bimatrix　game　for　both　players　are　intervals　as　well　from　the　viewpoint　of　logic.　Based　on　the　definition　of　the　values　of　the　bimatrix　game　for　players,　the　game　values　may　be　regarded　as　functions　of　payoffs　belonging　to　the　payoff　intervals,　which　are　proven　to　be　monotonic　non-decreasing.　A　pair　of　auxiliary　bilinear　programming　models　is　formulated　to　obtain　the　upper　bound　and　the　lower　bound　of　the　interval-type　values　of　the　interval-valued　bimatrix　game　by　using　the　upper　bounds　and　the　lower　bounds　of　the　payoff　intervals,　respectively.　A　real　example　of　the　engineering　project　management　problem　is　used　to　illustrate　the　applicability　and　effectivity　of　the　proposed　models　and　method.　Copyright　©　2015,　IGI　Global.