A　two-degree-of-freedom　coupled　Duffing　system　with　time　delay　is　studied　by　a　modified　homotopy　analysis　method.　First,　a　detailed　calculation　is　given　for　the　system.　Second,　single　periodic　and　period-doubling　solutions　are　obtained　by　solving　the　constructed　nonlinear　algebraic　equation.　Third,　upon　comparison　of　the　periodic　solution　obtained　by　the　multi-frequency　homotopy　analysis　method　with　the　numerical　solutions　obtained　by　the　numerical　method,　it　is　found　that　the　approximate　solution　agrees　well　with　the　numerical　solution　for　the　system.　Finally,　we　discuss　the　convergence　control　parameters　and　convergence　control　function.