In　the　paper,　we　design　an　adaptive　algorithm　for　non-submodular　set　function　maximization　over　a　single　matroid　constraint.　We　measure　the　deviation　of　the　set　function　from　fully　submodular　with　the　help　of　the　generic　submodularity　ratio　gamma.　The　adaptivity　quantifies　the　information　theoretic　complexity　of　oracle　optimization　for　parallel　computations.　We　propose　a　new　approximation　algorithm　based　on　the　continuous　greedy　approach　and　prove　that　the　algorithm　could　obtain　a　fractional　solution　with　approximation　ratio　(1　-　e(-gamma　2)　-　O(epsilon))　in　O(log　n　log(k/gamma　epsilon)/epsilon(-2)　log　n　log(1/gamma)　-　epsilon(-1)　log(1-epsilon))　then　use　the　contention　resolution　schemes　to　convert　the　fractional　solution　to　a　discrete　one　with　gamma　(1　-　e(-1))(1　-　e(-gamma　2)　-　O(epsilon))-approximation.