In this study, a series of cyclic loading tests were performed on viscoelastic dampers (VED) composed of viscoelastic polymer composite material and thin steel plates to observe the variation of the mechanical properties under different loading conditions. A mathematical model was developed based on the Kelvin???Voigt and Bouc???Wen models to formulate the nonlinear force-displacement relationship of the viscoelastic damper. The accuracy of the proposed mathematical model was verified using the data obtained from the tests. The mathematical model was applied to analyze a reinforced concrete framed structure retrofitted with viscoelastic dampers. Nonlinear dynamic analysis results showed that the average maximum inter-story drift ratios of the retrofitted structure met the target limit state after installing the VED. In addition, both the maximum and residual displacements were significantly reduced after the installation of the VED.