We　propose　a　private　algorithm　for　the　problem　of　maximizing　a　submodular　but　not　necessary　monotone　set　function　over　a　down-closed　family　of　sets.　The　constraint　is　very　general　since　it　includes　some　important　and　typical　constraints　such　as　knapsack　and　matroid　constraints.　Our　algorithm　DIFFERENTIALLY　PRIVATE　MEASURE　Corm.iuous　GREEDY　is　proved　to　be　O(epsilon)-differential　private.　For　the　multilinear　relaxation　of　the　above　problem,　it　yields　(T　e(-T)-　o(1))-approximation　guarantee　with　additive　error　O　(2　Delta/epsilon　n4),　where　T　is　an　element　of　[0,　1]　is　the　stopping　time　of　the　algorithm,　A　is　the　defined　sensitivity　of　the　objective　function,　which　is　associated　to　a　sensitive　dataset,　and　n　is　the　size　of　the　given　ground　set.　For　a　specific　matroid　constraint,　we　could　obtain　a　discrete　solution　with　near　1/e-approximation　guarantee　and　same　additive　error　by　lossless　rounding　technique.　Besides,　our　algorithm　can　be　also　applied　in　monotone　case.　The　approximation　guarantee　is　(1　-　e(-T)-　0(1))　when　the　submodular　set　function　is　monotone.　Furthermore,　we　give　a　conclusion　in　terms　of　the　density　of　the　relaxation　constraint,　which　is　always　at　least　as　good　as　the　tight　bound　(1　-　1/e).