A new energy-dissipation system for frame-core tube structure equipped with outriggers was presented, in which vertical viscous dampers were inserted between the outrigger and the perimeter columns to make full use of the relatively big displacement of these two components. The mathematical models of the structural system were obtained with both the assumed mode shape method and the finite element method according to the simplified calculation diagram. Based on the modal damping ratio, the optimal damping constants of linear viscous dampers were determined with parametric analysis. Finally, the seismic response of a frame-core tube structure equipped with outrigger damping system was simulated. It has been shown that the outrigger damping system can significantly increase the modal damping ratios of structures, and effectively decrease the dynamic response of structures.