An apparatus for cooling a spent fuel pool having a heat exchanger includes a cooling water pool positioned above the spent fuel pool; a floating device configured to be elevated according to a water level of a cooling water in the spent fuel pool; and an emergency cooling water supply pipe configured to form a path through which the cooling water of the cooling water pool is moved to the spent fuel pool and configured to include a floating valve that opens or closes a flow passage of the cooling water in connection with the elevation of the floating device.