An icemaker for an ice supply system for preventing water from overflowing from the ice tray by vibration and/or shaking of the surrounding structure includes an icemaker, a container provided at a lower part of the icemaker and an ice chute for supplying the ice stored in the ice container. An ejector in the ice tray of the icemaker and a dropper device having an inclined upper surface at a side of the open top of the ice tray are provided for dropping the ice discharged upwardly by the ejector. The dropper has no gap or slot through which the ejector passes to prevent water overflow through the dropper. An overflow prevention device is provided at another side of the open top of the ice tray for preventing water filled in the ice tray from overflowing.