Based　on　the　shortcuts　to　adiabatic　passage,　we　propose　a　scheme　for　directly　implementing　a　controlled-not　(CNOT)　gate　in　a　cavity　quantum　electrodynamics　system.　Moreover,　we　generalize　the　scheme　to　realize　a　CNOT　gate　in　two　separate　cavities　connected　by　an　optical　fiber.　The　strictly　numerical　simulation　shows　that　the　schemes　are　fast　and　insensitive　to　the　decoherence　caused　by　atomic　spontaneous　emission　and　photon　leakage.　In　addition,　the　schemes　can　provide　a　theoretical　basis　for　the　manipulation　of　the　multiqubit　quantum　gates　in　distant　nodes　of　a　quantum　network.