The　concept　of　submodularity　finds　wide　applications　in　data　science,　artificial　intelligence,　and　machine　learning,　providing　a　boost　to　the　investigation　of　new　ideas,　innovative　techniques,　and　creative　algorithms　to　solve　different　submodular　optimization　problems　arising　from　a　diversity　of　applications.　However　pure　submodular　problems　only　represent　a　small　portion　of　the　problems　we　are　facing　in　real　life　applications.　To　solve　these　optimization　problems,　an　important　research　method　is　to　describe　the　characteristics　of　the　non-submodular　functions.　The　non-submodular　functions　is　a　hot　research　topic　in　the　study　of　nonlinear　combinatorial　optimizations.　In　this　paper,　we　combine　and　generalize　the　curvature　and　the　generic　submodularity　ratio　to　design　an　approximation　algorithm　for　two-stage　non-submodular　maximization　under　a　matroid　constraint.