To obtain molten steel by melting a cold iron source, such as iron scrap and reduced iron, in extremely good efficiency.

In the melting method of the cold iron source 11 in a melting furnace 1 by both of oxygen burner heating and arc heating, firstly, the heating of the cold iron source is started only with the oxygen burner 7, and successively but at least after melting down the cold iron source, the residual cold iron source is heated and melted by changing over from the oxygen burner heating into the heating with the arc generated with electrodes 5, 6. At this time, a preheating vessel directly connected to the melting furnace is arranged, and exhaust gas in the melting furnace 1 is introduced into the preheating vessel to preheat the cold iron source, and thus, the cold iron source can further efficiently be heated and melted.