It is known that a base-isolated building exhibits a large response to a long-duration, long-period wave and an inter-connected system without base-isolation shows a large response to a pulse-type wave. To compensate for each deficiency, a new hybrid passive control system is investigated in which a base-isolated building is connected to another building (free wall) with oil dampers. It is demonstrated that the present hybrid passive control system is effective both for pulse-type ground motions and long-duration and long-period ground motions and has high redundancy and robustness for a broad range of disturbances.