The invention discloses a stable and quick automatic water replenishing system of a torch water-sealed tank. A first water replenishing pipeline and a second water replenishing pipeline are respectively connected between a water replenishing tank and the water-sealed tank; a first control valve is arranged on the first water replenishing pipeline; a second control valve is arranged on the second water replenishing pipeline; a first liquid level indication controller is arranged on the water-sealed tank; the first control valve and the second control valve are respectively interlocked with the first liquid level indication controller; when the liquid level of the water-sealed tank falls to a first set liquid level, the first liquid level indication controller controls the first control valve to be opened; when the liquid level of the water-sealed tank falls to a second set liquid level, the first liquid level indication controller controls the second control valve to be opened; when the liquid level of the water-sealed tank rises to a third set liquid level, the first liquid level indication controller controls the first control valve and the second control valve to be closed; the first set liquid level is higher than the second set liquid level; and the third set liquid level is higher than the first set liquid level.