An electric arc melting furnace includes a furnace shell (1) with an electrode (3) for melting scrap by heat of arc, an air blasting port (20) for blasting air, oxygen or oxygen-enriched air into the furnace shell (1) through an air control valve (19), a carbon blasted quantity indicator (CI) for measuring quantity of carbon to be charged into the furnace shell (1), a scrap charged quantity indicator (SI) for measuring quantity of the scrap charged into the furnace shell (1), an oxygen blasted quantity indicator (OI) for measuring quantity of oxygen blasted into the furnace shell (1) and an arithmetic processor (7) for computing quantity of air required for complete combustion of carbon monoxide (23) in the furnace shell (1) in response to measured value from the indicators (CI)(SI)(OI) to control a degree of opening of the air control valve (19). Air with quantity in proportion to the carbon monoxide (23) is blasted through the air blasting port (20), which enables control of combustion temperature in the furnace shell (1) and control of temperature in the scrap preheating device.