The　stabilities　of　fusion　frames　under　operator　perturbation　(simple　named　operator　perturbation　of　the　fusion　frames),　is　the　study　object　of　this　paper.　We　provide　a　way　as　follows　for　studying　the　operator　perturbation　of　fusion　frames.　Firstly,　we　consider　the　operator　perturbation　of　fusion　frame　sequences　by　the　gap　between　two　closed　subspaces　and　discuss　the　relationships　between　the　operator　perturbation　of　fusion　frames　and　the　operator　perturbation　of　fusion　frame　sequences.　Lastly,　we　transform　the　operator　perturbation　of　fusion　frames　into　the　operator　perturbation　of　fusion　frame　sequences　based　on　these　relationships.　Our　results　obtained　this　way　generalize　the　remarkable　results　which　have　been　obtained　by　Casazza,　Kutyniok,　Asgari,　Gavruta　and　Zhu.　©　2014　Elsevier　Inc.