We　study　one-step　implementation　of　the　Fredkin　gate　in　a　bi-modal　cavity　under　both　resonant　and　large　detuning　conditions　based　on　quantum　Zeno　dynamics,　which　reduces　the　complexity　of　experiment　operations.　The　influence　of　cavity　decay　and　atomic　spontaneous　emission　is　discussed　by　numerical　calculation.　The　results　demonstrate　that　the　fidelity　and　the　success　probability　are　robust　against　cavity　decay　in　both　models　and　they　are　also　insensitive　to　atomic　spontaneous　emission　in　the　large　detuning　model.　In　addition,　the　interaction　time　is　rather　short　in　the　resonant　model　compared　to　the　large　detuning　model.　©　Rinton　Press.