In　this　paper　we　investigate　the　necessary　condition　for　the　existence　of　the　periodic　solution　of　honeycomb　sandwich　plate　dynamic　system　of　two-degree-of-freedom.　We　establish　the　curvilinear　coordinates　frame　on　closed　orbits　of　the　unperturbed　system　of　the　honeycomb　sandwich　plate　dynamic　system　and　construct　successor　function.　Then　we　get　the　necessary　condition　of　the　existence　of　periodic　solution　by　judging　the　existence　of　the　successor　functions.　The　existence　of　periodic　solutions　is　important　for　studying　the　stability　of　sandwich　plates.