Submodular　optimization　has　been　well　studied　in　combinatorial　optimization.　However,　there　are　few　works　considering　about　non-submodular　optimization　problems　which　also　have　many　applications,　such　as　experimental　design,　some　optimization　problems　in　social　networks,　etc.　In　this　paper,　we　consider　the　maximization　of　non-submodular　function　under　a　knapsack　constraint,　and　explore　the　performance　of　the　greedy　algorithm,　which　is　characterized　by　the　submodularity　ratio　beta　and　curvature　alpha.　In　particular,　we　prove　that　the　greedy　algorithm　enjoys　a　tight　approximation　guarantee　of　(1　-　e(-alpha　beta))/alpha　for　the　above　problem.　To　our　knowledge,　it　is　the　first　tight　constant　factor　for　this　problem.　We　further　utilize　illustrative　examples　to　demonstrate　the　performance　of　our　algorithm.