In　this　paper　we　mainly　study　the　stabilities　of　K-frames　under　the　operator　perturbation.　Firstly,　we　provide　several　sufficient　conditions　of　the　operator　perturbation　for　a　K-frame　by　using　a　bounded　linear　operator　T　from　H1　to　H2.　We　also　give　an　equivalent　characterization　of　the　operator　perturbation　for　a　tight　K-frame.　Meanwhile,　we　correct　two　results　which　were　obtained　by　Ramu.　Lastly,　we　show　that　a　K-frame　can　construct　a　T-frame　by　the　perturbation　of　a　bounded　linear　operator　T.　Our　results　generalize　the　remarkable　results　of　the　operator　perturbation　for　a　frame　which　were　obtained　by　Casazza,　Christensen,　etc.　when　we　take　K=　I.　©　2018,　Springer　Nature　Switzerland　AG.