The effect of a viscous damper on a dynamic response of a single story linear system with a uniaxial eccentricity is investigated. The main results are as follows : if dampers are installed effectively, torsional deflection can be made very small. Furthermore, as a result of examining the applicability of the CQC method, it turns out that the evaluation accuracy of a response is about 10%, when the elastic radius ratio became 1.2 or more. Moreover, the formula that gives the effective amount of arrangement of a damper is proposed.