We　propose　a　scheme　to　generate　a　Greenberger-Horn-Zeilinger　(GHZ)　state　of　four　atoms　trapped　in　a　two-mode　optical　cavity　via　an　adiabatic　passage.　The　scheme　is　robust　against　moderate　fluctuations　of　the　experimental　parameters.　Numerical　calculations　show　that　the　excited　probabilities　of　both　the　cavity　modes　and　the　atoms　are　tiny　and　depend　on　the　pulse　peaks　of　the　classical　laser　fields.　For　certain　decoherence　due　to　the　atomic　spontaneous　emission　and　the　cavity　decay,　there　exits　a　range　of　pulse　peaks　to　get　a　high　fidelity.