To fine and disperse the oxide in molten steel and to improve the quality of a steel product by using a solid oxygen ion conductor into the molten steel and supplying and adding the oxygen with the impression of voltage or blowing oxidizing gas into the molten steel.

The solid oxygen ion conductor is used into the molten steel and an oxygen pump is formed with the impression of voltage, and the oxygen is supplied and added or the oxidizing gas is blown into the molten steel to produce oxide, but such supplying degree as not to oxidize the molten steel itself into FeO by giving excess oxygen, is restrained. That is, the oxygen needed to oxidize Al, Ti, Si, etc., contained in the molten steel is supplied and added. Such a metallic element as Al, Ti, Si, etc., has intense affinity with the oxygen, and while avoiding the oxidation of the molten steel itself by restraining to the supply of so sufficient oxygen quantity as to oxidize these elements, only the target metallic elements can selectively be oxidized.