A cooker includes a steam generator that supplies steam into a cooking chamber of the cooker. The steam generator includes a heating chamber having a heating space; a steam discharge port through which steam in the heating space is discharged; a residual water discharge port through which steam water in the heating space is discharged; a heater that heats the heating space; and a residual water discharge pipe connected with the residual water discharge port and that selectively discharges steam water from the heating space to an outside. A first end of the residual water discharge pipe is connected with the residual water discharge port, a second end of the residual water discharge pipe is arranged lower than the residual water discharge port, and a portion of the residual water discharge pipe between the first and second ends is arranged higher than the residual water discharge port.