Abstract: A cylindrical vibration-damping device equipped with an outer bracket, the outer bracket having a structure in which a press-fit member is press fit into a peripheral wall of a bracket body. A primary inner projection is provided at one axial end of the peripheral wall, while a secondary inner projection is provided at another axial end thereof. The outer bracket also includes a positioning section that is provided through mutual contact of axially opposing surfaces of the bracket body and the press-fit member and that determines a position of the press-fit member. The press-fit member which is molded as a thick-walled molded part has a thick contact surface formed on a tip end of the press-fit member in a direction of press fitting, and the thick contact surface comes into contact with a vibration damping rubber in the axial direction.