A method of operating an auger ice-making machine having a refrigeration casing, an auger screw rotatably disposed inside the casing and feeding, while scraping, the ice frozen on an inner wall surface of the casing, a stocker for storing/retaining the ice fed, the stocker being formed with an ice discharge port of the stocker in order to discharge the ice to an exterior of the machine by being opened, and a stored-ice detector for detecting a high level, and a low level, of a quantity of ice stored within the stocker, wherein: when the stored-ice detector detects the high level, a controller is activated to stop ice-making operation, and when the quantity of ice stored decreases below the low level by a required quantity, the controller restarts the ice-making operation; and when the controller judges, during a stopped state of the ice-making operation, that a block of ice has occurred in the stocker, the controller restarts the ice-making operation, provided that the stored-ice detector has detected the low level.