Referring to Figs. 2, 3 and 4, reference numeral (10) refers to a graphite electrode among three graphite electrodes that correspond to a three-phase AC power source. A graphite electrode is connected to each of the graphite electrodes (10) via a nipple. An electric current is supplied to these electrodes in an arc furnace of melt and refine metals. The invention deals with a method of refining and melting metals and a cooling apparatus used therefor, wherein, during the refining, a cooling liquid (11) which substantially consists of water is continuously sprayed onto the outer periphery (10a) of at least one graphite electrode (10) among the three graphite electrodes or, more particularly, onto the outer periphery (10a) of the graphite electrode (10) between an electrode holder and a furnace cover. In this case, the cooling liquid (11) is sprayed not in parallel with a horizontal level L-L, but upward or downward at an angle of 10° to 35° with respect to the level L-L to cool the electrode.