Cloud　storage　has　gained　great　attention　in　recent　years.　It　brings　many　benefits　as　well　as　security　issues.　Cloud　auditing　technology　can　ensure　the　integrity　of　cloud　users＇　data.　However,　it　lacks　efficiency　when　dealing　with　the　migration　scenario　of　a　large　amount　of　cloud　data.　In　this　paper,　we　propose　an　efficient　cloud　auditing　scheme　which　supports　data　migration　auditing.　We　first　construct　a　privacy-preserving　auditing　scheme　that　can　audit　cloud　data　during　data　migration,　which　can　hugely　reduce　the　migration　cost　when　data　corruption　happens.　We　further　extend　the　scheme　to　support　data　update　during　auditing.　By　supporting　batch　auditing　for　multiple　cloud　users＇　migration　auditing　tasks,　our　scheme　could　hugely　improve　the　efficiency.　Performance　analysis　demonstrates　that　our　auditing　scheme　is　secure　and　efficient.　Copyright　©　2017　Inderscience　Enterprises　Ltd.