The　0-1　linear　knapsack　problem　with　a　single　continuous　variable　(KPC)　is　an　extension　of　the　binary　knapsack　problem　(KP).　It　is　an　NP-hard　problem.　In　this　paper,　we　show　that　KPC　can　be　reduced　to　KP　and　a　pseudo-knapsack　problem　(PKP),　which　is　similar　to　the　traditional　knapsack　problem　except　that　the　profits　of　items　may　be　non-positive,　and　the　weight　sum　has　two　sided　limits　on　capacity.　We　use　the　Dynamic　Programming　algorithm　COMBO　(Martello　et　al.,　Manag　Sci　45(3):414-424,　1999)　to　solve　KP,　and　modify　the　branch　and　bound　method　EXPKNAP　(Pisinger,　Eur　J　Oper　Res　87:175-187,　1995)　for　KP　to　solve　the　PKP.　Numerical　experiments　show　the　efficiency　of　our　method.　©　2011　Springer　Science+Business　Media,　LLC.