We　study　the　problem　of　maximizing　a　monotone　non-submodular　function　under　a　d　knapsack　constraint　on　the　integer　lattice.　We　propose　three　streaming　algorithms　to　approach　this　problem.　We　first　design　a　two-pass　min{alpha(1　-　epsilon)/2(alpha+1)d,　1　-　1/alpha(w)2(alpha)　-　epsilon}-approximate　algorithm　with　total　memory　complexity　O(log　d　beta(-1)/beta　epsilon),　and　total　query　complexity　for　each　element　O(log　||　B　||(infinity)　log　d　beta(-1)/epsilon).　The　algorithm　relies　on　a　binary　search　technique　to　determine　the　amount　of　the　current　elements　to　be　added　into　the　output　solution.　It　also　requires　to　have　a　good　estimate　of　the　optimal　value,　we　use　the　maximum　value　of　the　unit　standard　vector　which　can　be　obtained　by　reading　a　round　of　data　to　construct　a　guess　set　of　the　optimal　value.　Then,　we　modify　our　algorithm　to　avoid　a　repetitive　reading　of　data　by　dynamically　update　the　maximum　value　of　the　unit　vector　along　with　the　coming　elements,　and　obtain　a　one-pass　streaming　algorithm　with　same　approximate　ratio.　Moreover,　we　design　an　improved　StreamingKnapsack　algorithm　to　reduce　the　memory　complexity　to　O(d/epsilon(2)).