We　propose　a　scheme　for　generating　atomic　NOON　states　via　adiabatic　passage.　In　the　scheme,　a　double　Lambda-type　three-level　atom　is　trapped　in　a　bimodal　cavity,　and　two　sets　of　Lambda-type　three-level　atoms　are　translated　into　and　outside　of　two　single-mode　cavities,　respectively.　The　three　cavities　connected　by　optical　fibers　are　always　in　vacuum　states.　After　a　series　of　operations　and　suitable　interaction　time,　we　can　obtain　arbitrary　large-n　NOON　states　of　two　sets　of　Lambda-type　three-level　atoms　in　distant　cavities　by　performing　a　single　projective　measurement　on　the　double　Lambda-type　three-level　atom.　Our　scheme　is　robust　against　the　spontaneous　emissions　of　atoms,　the　decays　of　fibers,　and　photon　leakage　of　cavities,　due　to　the　adiabatic　elimination　of　atomic　excited　states　and　the　application　of　adiabatic　passage.