The analysis of vibration response of structure with TMD is carried out under earthquake ,considering the ground-structure interaction. The varying rule of square difference of displacement of structure with the TMD on or off by changing the first inherent frequency is also presented .It has been proved by comparing and analyzing that a TMDstructure with optimum parameters can efficiently reduce the vibration of structure under strong wind and earthquake,when the main frequency of the ground motion is within the range of TMD vibration reducing frequency.