The ideal design of passive controlled building is that its mainframe remains elastic. However, it is necessary to consider the plasticity of its mainframe for there might be occurrences of seismic ground motions that are beyond assumptions. It is essential to evaluate the accumulated damage of damper from several oscillations caused by long-period and longduration ground motions during earthquakes. This paper proposes an energy balance-based response prediction method that considers the extent of plastic deformation of the mainframe with hysteretic dampers. The results from this proposed prediction method corresponds well to those of the time history response analysis.