Emerging　applications　such　as　optimal　budget　allocation　and　sensor　placement　impose　problems　of　maximizing　variants　of　submodular　functions　with　constraints　under　a　streaming　setting.　In　this　paper,　we　first　devise　a　streaming　algorithm　based　on　Sieve-Streaming　for　maximizing　a　monotone　diminishing　return　submodular　(DR-submodular)　function　with　a　cardinality　constraint　on　the　integer　lattice　and　show　it　is　a　one-pass　algorithm　with　approximation　ratio　1/2　-　epsilon.　The　key　idea　to　ensure　one　pass　for　the　algorithm　is　to　combine　binary　search　for　determining　the　level　of　an　element　with　the　exponential-growth　method　for　estimating　the　OPT.　Inspired　by　Sieve-Streaming++,　we　then　improve　the　memory　of　the　algorithm　to　O(k/epsilon)　and　the　query　complexity　to　O(k　log(2)　k/epsilon).