A method of fabricating a carbon electrode for melting quartz glass, wherein a kneaded material is obtained by heating and kneading a carbonaceous raw material and a binding material, and is pulverized, said carbonaceous raw material having a maximum particle diameter of 150 μm or less, and 90 wt % or more thereof being 75 μm or less of the particle diameter and said binding material having residual carbon of 50% or more, and thereafter a secondary particle is sieved such that the maximum particle diameter is 500 μm or less, and 50 wt % or more is 38 to 500 μm of the particle diameter, and pressing said secondary particle by cold isostatic pressing, followed by, after baking said pressed secondary particle, processing an isotropic graphite material graphitized at 2900 to 3100° C. and carrying out a purifying process on said isotropic graphite material.