Federated　learning　allows　a　large　number　of　participants　to　collaboratively　train　a　global　model　without　sharing　participant＇s　local　data.　Participants　train　local　models　with　their　local　data　and　send　gradients　to　the　cloud　server　for　aggregation.　Unfortunately,　as　a　third　party,　the　cloud　server　cannot　be　fully　trusted.　Existing　research　has　shown　that　a　compromised　cloud　server　can　extract　sensitive　information　of　participant＇s　local　data　from　gradients.　In　addition,　it　can　even　forge　the　aggregation　result　to　corrupt　the　global　model　without　being　detected.　Therefore,　in　a　secure　federated　learning　system,　both　the　privacy　and　aggregation　correctness　of　the　uploaded　gradients　should　be　guaranteed.　In　this　article,　we　propose　a　secure　and　efficient　federated　learning　scheme　with　verifiable　weighted　average　aggregation.　By　adopting　the　masking　technique　to　encrypt　both　weighted　gradients　and　data　size,　our　scheme　can　support　the　privacy-preserving　weighted　average　aggregation　of　gradients.　Moreover,　we　design　the　verifiable　aggregation　tag　and　propose　an　efficient　verification　method　to　validate　the　weighted　average　aggregation　result,　which　greatly　improves　the　performance　of　the　aggregation　verification.　Security　analysis　shows　that　our　scheme　is　provably　secure.　Extensive　experiments　demonstrate　the　efficiency　of　our　scheme　compared　with　the　state-of-The-Art　approaches.　　©　2013　IEEE.