For the nonlinear vibration system，if the derived system can reach synchronization with the original system by linear coupling， a corresponding anticipated system can be formed to realize the anticipated synchronization. The response of anticipated system can synchronize with the future response of original system and realize the prediction for nonlinear response，even for chaos in the originalsystem. In order to realize a long-term prediction， a series of anticipated systems can be formed by the rule presented in this paper. For chaotic motion in Duffing system， a 6-level anticipated system is formed， which can predict the response of original Duffing system in about 3s.