We　propose　a　scheme　to　realize　a　three-qubit　Toffoli　gate　with　three　atoms　held　in　separate　cavities　that　are　coupled　by　optical　fibers.　The　gate　is　achieved　by　engineering　an　effective　asymmetric　X-Y　model　induced　by　virtually　manipulating　the　atomic　excited　states　and　photons.　We　study　the　validity　of　the　scheme　as　well　as　the　influence　of　dissipation　by　numerical　simulation,　and　show　that　the　scheme　is　robust　against　decoherence.　(C)　2014　Optical　Society　of　America