We　propose　a　protocol　to　generate　Greenberger-Horne-Zeilinger　(GHZ)　and　W　states　of　three　atoms　trapped　in　only　one　cavity　The　setup　involves　one　cavity　and　linear　optical　elements　The　quantum　information　of　each　qubit　is　skillfully　encoded　on　the　degenerate　ground　states　of　the　three　different　atoms　hence　the　entanglement　between　them　is　relatively　stable　against　spontaneous　emission　The　advantages　of　the　protocol　are　their　robustness　against　detection　inefficiency　and　asynchronous　emission　of　the　photons　We　discuss　the　issue　related　to　the　practical　implementation　and　show　that　the　protocol　is　accessible　within　the　current　cavity　QED　technology　and　linear　optical　technology　Crown　Copyright　(C)　2010　Published　by　Elsevier　B　V　All　rights　reserved