In this paper, the vibration control effect of the exterior-installation Kagome damping syste (EKDS) was investigated by applying the Kagome dampers to a 15-story frame apartment building structure. The numerical analysis results of a structure with exterior-installation Kagome damping system up to the third story showed that the application story should be higher than second story to effectively reduce the base shear and the maximum drift of the uppermost story. When the exterior-installation Kagome damping system was installed up to the fifth story, the application story should be higher than third story and for obtaining the target performance.