In　the　paper,　we　design　a　privacy　algorithm　for　maximizing　a　general　submodular　set　function　over　a　down-monotone　family　of　subsets,　which　includes　some　typical　and　important　constraints　such　as　matroid　and　knapsack　constraints.　The　technique　is　inspired　by　the　measured　continuous　greedy　(MCG)　which　compensates　for　the　difference　between　the　residual　increase　of　elements　at　a　given　point　and　the　gradient　of　it　by　distorting　the　original　direction　with　a　multiplicative　factor.　It　directly　makes　the　continuous　greedy　approach　fit　to　the　problem　of　maximizing　a　non-monotone　submodular　function.　We　generate　the　MCG　algorithm　in　the　framework　of　differential　privacy.　It　is　accepted　as　a　robust　mathematical　guarantee　and　can　provide　the　protection　to　sensitive　and　personal　data.　We　propose　a　1/e-approximation　algorithm　for　the　general　submodular　function.　Moreover,　for　monotone　submodular　objective　functions,　our　algorithm　achieves　an　approximation　ratio　that　depends　on　the　density　of　the　polytope　defined　by　the　problem　at　hand,　which　is　always　at　least　as　good　as　the　previously　known　best　approximation　ratio　of　1　-　1　/　e.　©　2021,　Springer　Nature　Switzerland　AG.