The　study　of　non-submodular　maximization　on　the　integer　lattice　is　an　important　extension　of　submodular　optimization.　In　this　paper,　streaming　algorithms　for　maximizing　non　-negative　monotone　non-submodular　functions　with　knapsack　constraint　on　integer　lattice　are　considered.　We　first　design　a　two-pass　StreamingKnapsack　algorithm　combining　with　BinarySearch　as　a　subroutine　for　this　problem.　By　introducing　the　DR　ratio　gamma　and　the　weak　DR　ratio　gamma　w　of　the　non-submodular　objective　function,　we　obtain　that　the　approximation　ratio　is　min{gamma　2(1　-　epsilon)/2　gamma　+1,　1　-　1/gamma　w2　gamma　-　epsilon},　the　total　memory　complexity　is　O　(K　log　K　/epsilon),　and　the　total　query　complexity　for　each　element　is　O　(log　K　log(K/epsilon　2)/epsilon).　Then,　we　design　a　one-pass　streaming　algorithm　by　dynamically　updating　the　maximal　function　value　among　unit　vectors　along　with　the　currently　arriving　element.　Finally,　in　order　to　decrease　the　memory　complexity,　we　design　an　improved　StreamingKnapsack　algorithm　and　reduce　the　memory　complexity　to　O　(K　/epsilon　2).(c)　2022　Elsevier　B.V.　All　rights　reserved.