A small steam generator uses a cylindrical steam generation vessel having a steam generation portion formed to store an amount of water for generating steam and a steam passage portion formed on the upper end of the steam generation portion for spouting steam generated in the steam generation portion. A heater element is disposed within the steam generation vessel, and an induction heating coil is wound around the periphery of the steam generation vessel for energizing the heater element. The heater element is energized by supply of electric power to the heating coil so that steam generated by boiling of the water in the steam generation portion spouts upward from the steam passage. In the steam generator, a steam discharge duct is mounted on the upper end of the steam passage for receiving the steam spouting upward from the steam passage and to discharge it in a lateral direction such that drops of hot water adhered to a ceiling surface of the discharge duct fall and re-circulate back into the steam generation part.