Improving earthquake resistance of power plants has been important since Great East Japan earthquake occurred in 2011. In particular, thermal power plants accounted for most of the current Japanese power supply. Thus, improving earthquake resistance of the thermal power plants has been paid attention than other power plants. In current coal-fired power plants, boilers are simply suspended from the top of the support structures. Therefore, boilers easily vibrate. In order to suppress vibration of boilers during earthquakes, stoppers made of steel are installed between a boiler and its support structure. The stoppers dissipate vibration energy by plastic deformation. Therefore, the stoppers are effective in earthquakes with relatively small numbers of repeat counts, but may not effect in earthquakes with relatively large numbers of repeat counts. Then we propose installation vibration control dampers in support structure to suppress more the vibration and perform also in the repetition of earthquakes. In this paper, a seismic response analysis using analytical models of the boiler structure is conducted. In addition, a vibration control damper suitable for installed in the support structure are considered. As a result, a rectangle hysteresis damper is suitable as vibration control damper for the support structure.