A steam cooking apparatus, wherein a steam generating device is disposed halfway in an external circulation passage formed on the outside of a heating chamber and steam is supplied to the heating chamber through the external circulation passage. A control device controls a steam generating heater disposed in the steam generating device and a gas temperature heating heater installed in the external circulation passage at a position where air flow is circulated into the heating chamber. A cooking sequence is formed solely by a heating mode (heating mode A) by superheated steam obtained by increasing the temperature of the steam with the gas temperature increasing heater or a heating mode (heating mode B) by hot air or radiant heat obtained by heating the gas temperature increasing heater without steam or by the combination of these heating modes.