Maximizing　constrained　submodular　functions　lies　at　the　core　of　substantial　machine　learning　and　data　mining.　Specially,　the　case　that　the　data　come　in　a　streaming　fashion　receives　more　attention　in　recent　decades.　In　this　work,　we　study　the　approximation　algorithm　for　maximizing　a　non-decreasing　set　function　underd-knapsack　constraint.　Based　on　the　diminishing-return　ratio　for　set　functions,　a　non-trivial　algorithm　is　devised　for　maximizing　the　set　function　without　submodularity.　Our　results　cover　some　known　results　and　provide　an　effective　method　for　the　maximization　on　set　functions　no　matter　they　are　submodular　or　not.　We　also　run　the　algorithm　to　handle　the　application　of　support　selection　for　sparse　linear　regression.　Numerical　results　show　that　the　output　quality　of　the　algorithm　is　good.