An address translation cache (ATC) is configured to store translation entries indicating mapping information between a virtual address and a physical address of a memory device. The ATC includes a plurality flexible page group caches, a shared cache and a cache manager. Each flexible page group cache stores translation entries corresponding to a page size allocated to the flexible group cache. The shared cache stores, regardless of page sizes, translation entries that are not stored in the plurality of flexible page group caches. The cache manager allocates a page size to each flexible page group cache, manages cache page information on the page sizes allocated to the plurality of flexible page group caches, and controls the plurality of flexible page group caches and the shared cache based on the cache page information.