An ice maker and a water purifier capable of making ice using two water trays. The water purifier having an ice maker includes a water tray member comprising an ice-making water tray holding ice-making raw water to make ice using an ice-making unit, and an auxiliary water tray holding ice-making raw water remaining in the ice-making water tray in the course of cooling the ice-making raw water by means of the ice-making unit and removing the ice-making raw water from the ice-making water tray; an ice reservoir storing ice made in the ice-making unit; a cold water storage tank cooling water held therein using the ice made in the ice-making unit; and a guide member guiding the ice made in the ice-making unit so that the ice is selectively fed to either the ice reservoir or the cold water storage tank.