Vibration control devices are classified into passive, semi-active and active device. TMD(Tuned Mass Damper) is one of the passive control device that is mainly used to reduce vibration level of building structure and bridge structure. In this study, the application of passive tuned mass damper(TMD) to seismic response control of dome structures has been investigated. Because star dome structure has primary characteristics of dome structures, star dome structure was used as an example dome structure that is subjected to horizontal or vertical seismic loads. From this numerical analysis, it is shown that seismic response are influenced by vibration modes and it is reasonable to install TMD to the dominant points of each mode. And it is found that the passive TMD could effectively reduce the seismic responses of dome structure.