A vibration-damping device comprising: a tubular first attachment member; a second attachment member that is configured to be attached to any one of a vibration generating portion and a vibration receiving portion; elastic bodies that connect the first attachment member and the second attachment member with each other; and a bracket that is configured to be connected to the remaining one of the vibration generating portion and the vibration receiving portion and is press-fitted into the first attachment member, wherein the second attachment member includes a stopper wall portion which surrounds the first attachment member from radially outside, wherein the stopper wall portion is constituted of an upper stopper wall portion on a side opposite to a lower part in which the elastic bodies are installed in a part facing the first attachment member in a transverse direction, and side stopper walls facing each other in both directions in a longitudinal direction of the first attachment member, wherein outer stopper elastic bodies are installed on an inner circumferential surface of the upper stopper wall portion, and wherein a penetration hole which is open toward the stopper wall portion is formed in the first attachment member, and stopper elastic bodies covering the penetration hole are installed on an inner circumferential surface of the first attachment member, wherein in the stopper elastic bodies, a recess portion is formed in a part positioned at a part in which no penetration hole is formed on the inner circumferential surface of the first attachment member, wherein covering elastic bodies integrally formed with the stopper elastic bodies, the elastic bodies, and the outer stopper elastic bodies are installed on an outer circumferential surface of the first attachment member throughout the entire region, characterized in that protrusion parts of the covering elastic bodies covering the penetration hole from the outer circumferential surface side of the first attachment member protrude and come into contact with the outer stopper elastic bodies by the stopper elastic bodies being elastically deformed by the bracket and protruding to the outer circumferential surface side of the first attachment member through the penetration hole, when the bracket is press-fitted into the first attachment member. a tubular first attachment member; a second attachment member that is configured to be attached to any one of a vibration generating portion and a vibration receiving portion; elastic bodies that connect the first attachment member and the second attachment member with each other; and a bracket that is configured to be connected to the remaining one of the vibration generating portion and the vibration receiving portion and is press-fitted into the first attachment member, wherein the second attachment member includes a stopper wall portion which surrounds the first attachment member from radially outside, wherein the stopper wall portion is constituted of an upper stopper wall portion on a side opposite to a lower part in which the elastic bodies are installed in a part facing the first attachment member in a transverse direction, and side stopper walls facing each other in both directions in a longitudinal direction of the first attachment member, wherein outer stopper elastic bodies are installed on an inner circumferential surface of the upper stopper wall portion, and wherein a penetration hole which is open toward the stopper wall portion is formed in the first attachment member, and stopper elastic bodies covering the penetration hole are installed on an inner circumferential surface of the first attachment member, wherein in the stopper elastic bodies, a recess portion is formed in a part positioned at a part in which no penetration hole is formed on the inner circumferential surface of the first attachment member, wherein covering elastic bodies integrally formed with the stopper elastic bodies, the elastic bodies, and the outer stopper elastic bodies are installed on an outer circumferential surface of the first attachment member throughout the entire region, characterized in that protrusion parts of the covering elastic bodies covering the penetration hole from the outer circumferential surface side of the first attachment member protrude and come into contact with the outer stopper elastic bodies by the stopper elastic bodies being elastically deformed by the bracket and protruding to the outer circumferential surface side of the first attachment member through the penetration hole, when the bracket is press-fitted into the first attachment member.