In a method of making a high-quality silica glass, a rare earth element that is a substance making a great contribution to the index of refraction is introduced therein together with aluminum for stabilizing the glass. An alkoxide of aluminum or its derivative is used as the starting material for preparing a boehmite sol. A salt of at least one element selected from rare earth elements or a solution in which the salt is dissolved and the boehmite sol are mixed with a silica sol, whereupon the sols are vitrified.