Two　schemes　of　implementing　the　Toffoli　gate　are　proposed　in　an　array　of　coupled　cavities.　In　the　first　one,　two　classical　laser　fields　with　fixed　Rabi　frequency　are　used　via　quantum　Zeno　dynamics.　While　in　the　second　scheme,　the　invariant-based　inverse　engineering　is　used　to　implement　the　Toffoli　gate,　which　can　drive　the　instantaneous　eigenstates　to　evolve　exactly　under　the　Schrodinger　equation.　The　strictly　numerical　simulations　are　given　and　the　influences　of　cavity　decay　and　spontaneous　emission　on　the　Toffoli　gate　operation　are　analyzed　with　master　equation.　The　result　shows　that　our　schemes　for　the　Toffoli　gate　are　robust　against　the　decoherence　because　of　the　short　time　needed.　©　2014　Taylor　&　Francis.