Federated　learning　(FL)　was　once　considered　secure　for　keeping　clients＇　raw　data　locally　without　relaying　on　a　central　server.　However,　the　transmitted　model　weights　or　gradients　still　reveal　private　information,　which　can　be　exploited　to　launch　various　inference　attacks.　Moreover,　FL　based　on　deep　neural　networks　is　prone　to　the　curse　of　dimensionality.　In　this　paper,　we　propose　a　compressed　and　privacy-preserving　FL　scheme　in　DNN　architecture　by　using　Compressive　sensing　and　Adaptive　local　differential　privacy　(called　as　CAFL).　Specifically,　we　first　compress　the　local　models　by　using　Compressive　Sensing　(CS),　then　adaptively　perturb　the　remaining　weights　according　to　their　different　centers　of　variation　ranges　in　different　layers　and　their　own　offsets　from　corresponding　range　centers　by　using　Local　Differential　Privacy　(LDP),　finally　reconstruct　the　global　model　almost　perfectly　by　using　the　reconstruction　algorithm　of　CS.　Formal　security　analysis　shows　that　our　scheme　achieves　eμ-LDP　security　and　introduces　zero　bias　to　estimating　average　weights.　Extensive　experiments　using　MINIST　and　Fashion-MINIST　datasets　demonstrate　that　our　scheme　with　minimum　compression　ratio　0.05　can　reduce　the　number　of　parameters　by　95%,　and　with　a　lower　privacy　budget　eμ　=　1　can　improve　the　accuracy　by　80%　on　MINIST　and　12.7%　on　Fashion-MINIST　compared　with　state-of-the-art　schemes.　©　2022　ACM.