Synthetic quartz glass is produced by feeding a silica-forming raw material gas, hydrogen gas, oxygen gas and a fluorine compound gas from a burner to a reaction zone, flame hydrolyzing the silica-forming raw material gas in the reaction zone to form fine particles of fluorine-containing silica, depositing the silica fine particles on a rotatable substrate in the reaction zone so as to create a fluorine-containing porous silica matrix, and heat vitrifying the porous silica matrix in a fluorine compound gas-containing atmosphere. This process enables the low-cost manufacture of a synthetic quartz glass having a higher and more uniform transmittance to light in the vacuum ultraviolet region than has hitherto been achieved.