There is provided a cooling apparatus for a molten core material, including: two or more cooling material containers disposed under a reactor vessel including a nuclear reactor core and including a cooling material therein; a first screen disposed under the two or more cooling material containers and including two or more first through-holes; and a second screen disposed under the first screen and including two or more second through-holes, wherein an average size of the two or more first through-holes is greater than an average size of the two or more second through-holes.