A vibration-damping device (1; 101; 301) comprising: a bracket member connected to one of a vibration-generator and a vibration-receiver; and a pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B), each vibration-damping member (2A, 2B; 102A, 102B; 302A, 302B) including: a cylindrical first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) connected to the one of the vibration-generator and the vibration-receiver via the bracket member, a second mounting member (21A, 21B) connected to the other of the vibration generator and the vibration receiver, and an elastic body (22A, 22B, 70A, 70B, 122A, 122B) that elastically connects the first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) and the second mounting member (21A, 21B), wherein first mounting members (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) are fitted inside a fitting part provided in the bracket member; the pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B) are disposed such that end faces of the first mounting members (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) in an axial direction thereof face each other, and second mounting members (21A, 21B) are formed in cylindrical shapes; a pair of sandwiching members (4A, 4B) are provided to sandwich the pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B) from both sides in an axial direction thereof, and a fastening member is provided to be inserted inside the second mounting members (21A, 21B) and to connect the pair of sandwiching members (4A, 4B); each first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) of the pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B) includes a flange part (23A, 23B, 61A, 61B) that protrudes radially outward; the bracket member is disposed between a pair of flange parts (23A, 23B, 61A, 61B); and by fastening the fastening member and thereby pressing the pair of sandwiching members (4A, 4B) in a direction closer to each other, the bracket member is sandwiched between the pair of flange parts (23A, 23B, 61A, 61B) and the pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B) are held in the bracket member, and elastic bodies are compressed beforehand by the pair of sandwiching members (4A, 4B); characterized in that the first mounting members (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) and the fitting part are each formed in a shape having a plurality of radii of different lengths in a plan view. a bracket member connected to one of a vibration-generator and a vibration-receiver; and a pair of vibration-damping members (2A, 2B; 102A, 102B; 302A, 302B), each vibration-damping member (2A, 2B; 102A, 102B; 302A, 302B) including: a cylindrical first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) connected to the one of the vibration-generator and the vibration-receiver via the bracket member, a second mounting member (21A, 21B) connected to the other of the vibration generator and the vibration receiver, and an elastic body (22A, 22B, 70A, 70B, 122A, 122B) that elastically connects the first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) and the second mounting member (21A, 21B), wherein first mounting members (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) are fitted inside a fitting part provided in the bracket member; a cylindrical first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) connected to the one of the vibration-generator and the vibration-receiver via the bracket member, a second mounting member (21A, 21B) connected to the other of the vibration generator and the vibration receiver, and an elastic body (22A, 22B, 70A, 70B, 122A, 122B) that elastically connects the first mounting member (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) and the second mounting member (21A, 21B), wherein first mounting members (20A, 20B, 60A, 60B, 120A, 120B, 220A, 220B) are fitted inside a fitting part provided in the bracket member;