This study investigates the seismic responses of two structures connected by a sky-bridge equipped with viscoelastic dampers (VED) at the bridge-building connections. The applicability of the method is verified first by observing RMS (root-mean-squared) responses of two-degrees-of-freedom systems subjected to white noise ground excitation. Then model structures with various number of stories are analyzed using earthquake ground motions to observe the effect of the varying size of VED on the reduction of dynamic responses. According to the analysis results, there exists a proper size of VED which minimizes the structural responses. It is also observed that the effectiveness of VED increases as the difference of natural frequencies between the two connected structures increases.