The　problem　of　submodular　maximization　on　the　integer　lattice　has　attracted　more　and　more　attention　due　to　its　deeply　applications　in　many　areas.　In　this　paper,　we　consider　maximizing　a　non-negative　monotone　non-submodular　function　with　knapsack　constraint　on　massive　data.　We　combine　two　proposed　algorithms　called　StreamingKnapsack　and　BinarySearch　for　this　problem　by　introducing　the　DR　ratio　gamma(d)　and　the　weak　DR　ratio　gamma(w)　of　the　non-submodular　objective　function.　Finally,　we　obtain　the　performance　guarantee　of　the　StreamingKnapsack　supplemented　by　a　simple　one-pass　algorithm,　with　the　approximation　ratio　of　the　better　output　of　them　as　min{gamma(2)(d)(1　-　epsilon)/2(gamma　d+1),　1　-　1/gamma(w)2(gamma　d)　-　epsilon}.　Meanwhile,　both　the　time　complexity　and　space　complexity　are　dependent　on　the　size　of　knapsack　capacity　K　and　epsilon　is　an　element　of　(0,　1).