A device for damping runout vibration of a rotating shaft system at least including a rotating shaft and a rotating body rotatably supported by the shaft. A ring (24) is provided outside a bearing (23) fitted on a rotating shaft with a clearance between the ring and an outer ring of the bearing. A vibration damping mechanism includes, in order to suppress runout vibration of a rotating shaft system from the radially outside of the ring (24), a blade spring (25) compressed by a preload and a stopper (26) for setting an operation limit of the blade spring.