The dynamic parameters obtained depending on the existing structural properties, material properties, boundary and damage condition are quite effective on the behavior of the structures under the effect of dynamic loads. These dynamic parameters have characteristic features for each structure. In this study, the effect of damping ratio, which is one of the dynamic characteristics, on the seismic behavior of historical structures was studied. For this aim, historical masonry Guesthouse Building belong to the Church of Santa Maria was selected to examined. Linear time history analyses were performed for three different damping ratios as 2%, 5%, and 10%. The horizontal component of Erzincan Earthquake (1992) was used in linear time history analyses. The maximum displacement, principal stress and strain values obtained from performed linear time history analyses for different damping ratios were compared. It is observed that, displacement, stress and strain values increase as the damping ratio decrease when the results are examined. It is concluded that, damping ratio is the important parameter for the evaluation of seismic response of historical masonry structures which are weak to external effect especially earthquake. Therefore, the damping ratios should be obtained with experimental tests before the numerical evaluation of seismic behavior.