The present invention provides a tubular vibration-damping mount capable of securing durability against an input in a direction perpendicular to an axis. A tubular vibration-damping mount comprises a core member, a tubular member, a rubber member, an upper surface of which has, as viewed in a cross section including an axis of the core member, a recessed portion in a radially inner direction of the rubber member and an inclined portion whose inclination angle is smoothly and upwardly increased in the radially inner direction from a point on the tubular member as a starting point, and a bracket, wherein the tubular member has, in an area higher than a lower end of an adhesion surface between the tubular member and the rubber member and the upper surface of the rubber member starts from a point on the inner periphery of the diameter-enlarged portion of the tubular member, which the point agrees with the starting point.