In　this　paper,　we　investigate　a　class　of　three　dimensional　nonlinear　dynamical　systems　whose　unperturbed　systems　have　a　family　of　periodic　orbits.　Firstly,　we　establish　the　moving　Frenet　Frame　on　these　closed　orbits.　Secondly,　the　successor　functions　are　defined　by　the　orbits　which　go　through　the　normal　plane.　Finally,　by　judging　the　existence　of　solutions　of　the　equations　obtained　from　the　Successor　functions,　we　obtain　the　necessary　condition　for　the　existence　of　periodic　solutions　of　these　three　dimensional　nonlinear　dynamical　systems.　The　result　has　important　significance　for　the　basic　research　of　applied　mechanics.