This vibration-damping device (1) includes: a bracket member (3) connected to one of a vibration-generator and a vibration-receiver; and a vibration-damping member (2A, 2B) including: a cylindrical first mounting member (20A, 20B) fitted inside a fitting part (30) provided in the bracket member (3), a second mounting member (21A, 21B) connected to the other of the vibration generator and the vibration receiver, and an elastic body (22A, 22B) that elastically connects the first mounting member (20A, 20B) and the second mounting member (21A, 21B). The first mounting member (20A, 20B) and the fitting part (30) are each formed in a shape having a plurality of radii of different lengths in a plan view.