The　problem　of　maximizing　a　given　set　function　with　a　cardinality　constraint　has　widespread　applications.　A　number　of　algorithms　have　been　provided　to　solve　the　maximization　problem　when　the　set　function　is　monotone　and　submodular.　However,　reality-based　set　functions　may　not　be　submodular　and　may　involve　large-scale　and　noisy　data　sets.　In　this　paper,　we　present　the　Stochastic-Lazier-Greedy　Algorithm　(SLG)　to　solve　the　corresponding　nonsubmodular　maximization　problem　and　offer　a　performance　guarantee　of　the　algorithm.　The　guarantee　is　related　to　a　submodularity　ratio,　which　characterizes　the　closeness　of　to　submodularity.　Our　algorithm　also　can　be　viewed　as　an　extension　of　several　previous　greedy　algorithms.