In this study, effectiveness of seismic retrofitting methods using passive damping devices was investigated through numerical analyses of short-period structures under earthquakes which have short-duration and high-frequency impulse characteristics similar to Geyongju earthquakes. Displacement spectra of elastic systems and ductility demand of inelastic systems were evaluated by increasing viscous or friction damping. The damping devices could reduce responses of the structures with shorter structural period than 0.2s. The earthquakes similar to impulse load did not induce the responses of the structures with longer period than 0.4s, and the effects of the damping devices which generates damping forces proportional to structural responses became insignificant.