An improvement in the Czochralski single crystal growing of a rare earth-gallium garnet such as gadolinium gallium garnet according to which the single crystal boules of a relatively large diameter and outstandingly free from any crystal defects and inclusions are readily obtained. The improved method comprises keeping the melt of the oxide mixture formed in an iridium crucible for at least 15 hours in the molten state before crystal growing is started. It was also shown that addition of certain additive gases, e.g. water vapor, carbon dioxide and oxygen, to the gaseous atmosphere mainly composed of, for example, nitrogen, in which crystal growing was performed, in a limited proportion was effective to further improve the crystal quality and to decrease the particulate inclusions in the single crystal boules.