A storage system performing an overwrite, a host system controlling the storage system, and an operating method of the storage system, wherein the storage system includes a memory device; and a controller that receives new data and an overwrite request from the host system, wherein the overwrite request includes a first logical address for old data and a second logical address for the new data, and performs an overwrite operation by writing the new data corresponding to the second logical address to the memory device and invalidating the old data corresponding to the first logical address according to the overwrite request.