Molten steel is refined in an electric furnace by using iron scrap as a main iron source, and is tapped into a separate refining vessel. Thereafter, metallic-Al containing material and CaO are added onto a bath surface of the molten steel, and an oxygen containing gas is supplied to the molten steel. Thereby, a nitrogen-removal reaction utilizing an AlN formation reaction is caused to proceed. Consequently, even in the case of molten steel having a low carbon content, a low-nitrogen steel can be refined and produced at low costs.