An ice maker and a controlling method thereof are provided. The system and method may prevent the overflow or splashing of water or thin ice out of an ice tray during the supply of water or when the ice maker is shaken by an external force. The ice maker may include an ice tray, and an ice tray cover that covers an open portion of the ice tray. The cover may include an opening through which water may be supplied to the ice tray, and through which ice may be discharged from the ice tray. The cover may move together with the tray, or may move separately from the tray, to facilitate these supply and discharge processes.