In　this　paper,　we　study　one　variant　of　the　multiobjective　knapsack　problem,　i.e.,　the　biobjective　0-1　linear　knapsack　problem　with　a　single　continuous　variable　(BKPC).　An　exact　algorithm,　the　biobjective　branch　and　bound　method　(BOBB),　is　presented　to　find　all　nondominated　points　of　the　BKPC.　We　analyze　the　nondominated　frontier　of　the　BKPC　and　design　a　new　branching　strategy　to　improve　the　algorithm.　Finally　an　illustrative　example　shows　how　the　algorithm　solves　a　practical　problem.　©　2017　IEEE.