The present invention relates to an improved process for providing the production of a glass preform for an optical fiber which includes substantially no bubbles therein and also which has a substantially uniform shape. The process for the production of a glass preform which comprises at least silica for an optical fiber is comprised of producing a body comprising a rod on which fine glass particles are deposited, preferably by a vapour phase reaction and heating the body to vitrify the body under a reduced atmosphere or a vacuum so that the glass preform is produced. The process includes a first heating step of degassing the body at a first heating temperature, a second heating step of shrinking the body at a second heating temperature which is higher than the first heating temperature and which is lower than a third heating temperature, and a third heating step of vitrifying the shrunken body at the third temperature which corresponds to a vitrification temperature of the fine glass particles so as to produce the glass preform.