Nowadays,　massive　amounts　of　data　are　growing　at　a　rapid　rate　every　moment.　If　data　can　be　processed　and　analyzed　promptly　as　they　arrive,　they　can　bring　huge　added　values　to　the　society.　In　this　paper,　we　consider　the　problem　of　maximizing　a　monotone　non-submodular　function　subject　to　a　cardinality　constraint　under　the　streaming　setting　and　present　a　linear-time　single-pass　deterministic　algorithm　for　this　problem.　We　analyze　the　algorithm　using　the　parameter　of　the　generic　submodularity　ratio　gamma　to　achieve　an　approximation　ratio　of　[gamma(4)/c(1+gamma+gamma(2)+gamma(3))　-　epsilon]　for　any　epsilon　＞=　0　with　the　query　complexity　[n/c]　+　c,　and　the　memory　complexity　is　O(ck　log(k)　log(1/epsilon)),　where　c　is　a　positive　integer.　When　gamma　=　1,　the　algorithm　achieves　the　same　ratio　for　the　submodular　version　of　the　problem　with　the　matching　query　complexity　and　memory　complexity.