A storage device, including: a nonvolatile memory device including a plurality of memory cells; and a controller configured to, based on receiving an open zone command from an external host device: based on a number of free erase units from among a plurality of erase units included in the plurality of memory cells being greater than a threshold value, allocate at least two free erase units to a first-type zone, and based on the number of the free erase units being smaller than or equal to the threshold value, allocate the at least two free erase units to a second-type zone. wherein the controller is further configured to permit a random write based on a random logical address received from the external host device for the first-type zone, and to permit a zone write based on a sequential logical address received from the external host device for the second-type zone.