In　this　paper,　we　study　the　bifurcation　of　periodic　solutions　for　a　four-dimensional　deployable　circular　mesh　antenna　system.　The　tools　for　proving　these　results　are　the　averaging　theory　and　Brouwer　degree　theory.　Based　on　constructing　displacement　maps,　we　study　the　bifurcation　of　the　periodic　solutions　of　linear　center,　and　to　discuss　the　maximum　number　of　periodic　solutions　in　certain　parameter　control　conditions.　The　results　in　this　paper　are　helpful　to　the　study　of　nonlinear　dynamic　characteristics　and　vibration　control　of　deployable　circular　mesh　antenna　model.