In　the　paper,　we　study　the　adaptivity　of　maximizing　a　monotone　nonsubmodular　function　subject　to　a　cardinality　constraint.　Adaptive　approximation　algorithm　has　been　previously　developed　for　the　similar　constrained　maximization　problem　against　submodular　function,　attaining　an　approximation　ratio　of　(1　-　1/e　-　epsilon)　and　O　(log　n/epsilon(2))　rounds　of　adaptivity.　For　more　general　constraints,　Chandra　and　Kent　described　parallel　algorithms　for　approximately　maximizing　the　multilinear　relaxation　of　a　monotone　submodular　function　subject　to　either　cardinality　or　packing　constraints,　achieving　a　near-optimal　(1　-　1/e　-　epsilon)approximation　in　O　(log(2)　m　log　n/epsilon(4))　rounds.　We　propose　an　Expand-Parallel-Greedy　algorithm　for　the　multilinear　relaxation　of　a　monotone　and　normalized　set　function　subject　to　a　cardinality　constraint　based　on　rounding　the　multilinear　relaxation　of　the　function.　The　algorithm　achieves　a　ratio　of　(1　-　e(-gamma　2)　-　epsilon)　,　runs　in　O　(log　n/epsilon(2))　adaptive　rounds　and　requires　O　((n　log　n/epsilon(2)))　queries,　where　gamma　is　the　Continuous　generic　submodularity　ratio.