To cool graphite electrodes by spraying of a coolant without generating hydrogen gas or the like through water gas reactions inside an electric-arc furnace by greatly reducing original electrode units through the minimizing of the oxidation wear of the graphite electrodes.

A current is passed to a line of graphite electrodes which comprises graphite electrodes 1 connected to one another via nipples. Above the furnace lid of an electric steelmaking furnace, a coolant 2 is sprayed toward the outer peripheries of the line of graphite electrodes as the coolant 2 is ejected at an inclination angle to a horizontal level of not more than 10° in the upward direction and up to 10° in the downward direction.