PURPOSE: A water purifier is provided to eliminate fine dust remaining in purified water and cool water using one filter without a separate filtering part in a purified water tank and a cool water tank. CONSTITUTION: A water purifier includes a purified water tank and a filtering part(10). The purified water tank stores purified water generated from a water purifying system. The filtering part purifies water from the purified water tank. The water purifier further includes a filter(15). The filter is installed in the filtering part and includes nano-alumina fiber. The filtering part includes a housing with an internal space. The water purifier further includes a cool water tank.