Although　submodular　maximization　generalizes　many　fundamental　problems　in　discrete　optimization,　lots　of　real-world　problems　are　non-submodular.　In　this　paper,　we　consider　the　maximization　problem　of　non-submodular　function　with　a　knapsack　constraint,　and　explore　the　performance　of　the　greedy　algorithm.　Our　guarantee　is　characterized　by　the　submodularity　ratio　β　and　curvature　α.　In　particular,　we　prove　that　the　greedy　algorithm　enjoys　a　tight　approximation　guarantee　of　(Formula　Presented)　for　the　above　problem.　To　our　knowledge,　it　is　the　first　tight　constant　factor　for　this　problem.　In　addition,　we　experimentally　validate　our　algorithm　by　an　important　application,　the　Bayesian　A-optimality.　©　Springer　Nature　Switzerland　AG　2019.