A steam cooking apparatus with improved water supply and drainage structures. The apparatus includes a body, a cooking compartment, a steam generator to supply steam into the cooking compartment, a water vessel to store water and supply the water into the steam generator, a water supply device including a holder and a slider slidably mounted in the holder so as to be withdrawn from the body, a first water supply tube connecting the slider and the water vessel, a second water supply tube connecting the water vessel and the steam generator, and a drain tube to drain water in the steam generator to the outside of the body. The drain tube includes an end fixed to the slider so that the end of the drain tube is withdrawn with the slider from the body when water in the steam generator is drained to the outside.