In　this　paper,　the　sufficient　condition　for　the　existence　of　periodic　solution　of　a　class　of　three　dimensional　nonlinear　dynamical　systems　is　investigated.　The　moving　Frenet　frame　is　established　on　the　closed　orbit　and　the　successor　functions　near　the　closed　orbit　are　defined.　According　to　the　study　of　the　existence　of　solution　of　the　equation　which　obtained　from　the　successor　functions　with　the　implicit　function　theorem,　the　sufficient　condition　for　the　existence　of　periodic　solution　of　these　systems　is　obtained.　The　results　in　this　paper　have　important　significance　to　decide　the　existence　of　periodic　solution　of　three　dimensional　nonlinear　dynamical　systems.　©　(2013)　Trans　Tech　Publications,　Switzerland.