Due　to　its　broad　applications,　maximizing　a　diminishing　return　submodular　function　with　a　knapsack　constraint　has　been　extensively　studied　recently.　In　the　paper,　we　mainly　consider　this　problem　on　the　integer　lattice.　Assuming　the　optimal　value　is　known,　we　first　design　a　one-pass　algorithm　and　prove　that　its　approximation　ratio　is　(1/3　-　epsilon).　Observing　the　difficult　of　actually　knowing　the　optimal　value,　we　design　a　streaming　algorithm　with　two　passes,　where　in　the　first　round　we　find　the　maximum　value　of　the　unit　vector　to　estimate　the　range　of　the　OPT.　Furthermore,　in　order　to　improve　the　performance　of　the　algorithm,　we　design　an　online　algorithm　called　DynamicMRT　to　reduce　the　number　of　rounds,　eventually　achieving　an　approximation　ratio　(1/3　-　epsilon),　a　memory　complexity　O(K　log　K\epsilon)　and　query　complexity　O(log(2)　K\epsilon)　per　element　for　the　knapsack　constraint　K.