A process for the vitrification of a porous glass preform for an optical fiber involves heating the preform under an increasing pattern of temperature in a vacuum furnace comprising a muffle tube. The increasing pattern is divided into two steps consisting of a first step and a subsequent second step. The first step has a pattern in which the heating temperature is increased under a reduced pressure atmosphere and a gas comprising at least an inert gas is supplied to the vacuum furnace under the reduced pressure atmosphere. The second step has a pattern in which the heating temperature is increased under a reduced pressure atmosphere in which a gas comprising a smaller amount of an inert gas than in the first step is supplied to the furnace or under a vacuum pressure atmosphere in which no gas is supplied to the furnace.