A liquid-tight vibration-damping device which includes: a tubular first attachment member joined to one of a vibration generating section and a vibration receiving section; a second attachment member joined to the other of the vibration generating section and the vibration receiving section; an elastic body configured to elastically join the first attachment member and the second attachment member; a partition member configured to partition a liquid chamber in the first attachment member in which a liquid is sealed into a first liquid chamber and a second liquid chamber; and a limiting passage formed in the partition member and configured to communicate the first liquid chamber and the second liquid chamber, wherein, the limiting passage includes: a main body passage disposed in the partition member, extending in the circumferential direction and defined by a first wall of the partition member which faces the first liquid chamber and a second wall thereof which faces the second liquid chamber; a first communication section configured to communicate the main body passage and the first liquid chamber; a second communication section configured to communicate the main body passage and the second liquid chamber, and at least one of the first communication section and the second communication section passes through the first wall or the second wall and has openings disposed in a passage direction of the main body passage, characterized in that the first communication section has first openings passing through the first wall as the openings, and diameters of the first openings gradually decrease toward the first liquid chamber. a tubular first attachment member joined to one of a vibration generating section and a vibration receiving section; a second attachment member joined to the other of the vibration generating section and the vibration receiving section; an elastic body configured to elastically join the first attachment member and the second attachment member; a partition member configured to partition a liquid chamber in the first attachment member in which a liquid is sealed into a first liquid chamber and a second liquid chamber; and a limiting passage formed in the partition member and configured to communicate the first liquid chamber and the second liquid chamber, wherein, the limiting passage includes: a main body passage disposed in the partition member, extending in the circumferential direction and defined by a first wall of the partition member which faces the first liquid chamber and a second wall thereof which faces the second liquid chamber; a first communication section configured to communicate the main body passage and the first liquid chamber; a second communication section configured to communicate the main body passage and the second liquid chamber, and at least one of the first communication section and the second communication section passes through the first wall or the second wall and has openings disposed in a passage direction of the main body passage, characterized in that the first communication section has first openings passing through the first wall as the openings, and diameters of the first openings gradually decrease toward the first liquid chamber. a main body passage disposed in the partition member, extending in the circumferential direction and defined by a first wall of the partition member which faces the first liquid chamber and a second wall thereof which faces the second liquid chamber; a first communication section configured to communicate the main body passage and the first liquid chamber; a second communication section configured to communicate the main body passage and the second liquid chamber, and at least one of the first communication section and the second communication section passes through the first wall or the second wall and has openings disposed in a passage direction of the main body passage, characterized in that the first communication section has first openings passing through the first wall as the openings, and diameters of the first openings gradually decrease toward the first liquid chamber.