Large-scale　deployable　space　spacecraft　structures　have　a　very　wide　range　of　appli-cations　in　the　field　of　spaceflight.　The　main　goal　of　this　study　is　to　investigate　the　maximum　number　of　periodic　solutions　for　a　four-dimensional　deployable　circular　mesh　antenna　model.　We　study　the　parameter　conditions　and　upper　bound　of　the　number　of　periodic　solutions　that　can　bifurcate　from　linear　center　by　the　averaging　theory　and　Brouwer　degree　theory.　The　results　in　this　paper　are　helpful　to　the　study　of　nonlinear　dynamic　characteristics　and　vibration　control　of　deployable　circular　mesh　antenna　model.