The purpose of this paper is to carry out a response evaluation of passive control structure with viscous dampers considering its performance decrement under long-period ground motion. An analytical model of the viscous damper is considered to evaluate its performance decrement caused by the long-period cyclic loading, and its accuracy is verified by comparing with test results. Time-history analysis of a 20-story model with the proposed viscous dampers is performed when the main frames are elastic and elasto-plastic. It is verified that we can safely evaluate the response using the proposed evaluation method of this study when the response is large.