A steam generator capable of preventing scale contained in air bubbles and water droplets generated in the course of boiling water by a heater from entering a steam ejection hole and a heating cooking apparatus having the steam generator is provided. The steam generator includes a steam container to store water and having at least one steam ejection hole formed at an upper location thereof, a heater adapted to heat the water stored in the steam container so as to generate steam, and a barrier unit provided below the steam ejection hole and adapted to prevent the air bubbles from entering the steam ejection hole. The barrier unit includes a base plate having a plurality of steam passage holes and a web plate coming into close contact with an inner wall surface of the steam container.