A synthetic quartz glass optical member for an ultraviolet laser, suitably applicable as a stepper lens of a lithographer using an excimer laser beam and other optical members, wherein the quartz glass has a hydroxyl content of 10 to 100 ppm, a chlorine content of 200 ppm or less, a hydrogen content of 1.times.10.sup.16 molecules/cm.sup.3 or less, a homogeneity of refractive index of 5.times.10.sup.-6 or less in terms of .DELTA.n, and a birefringence of 5 nm/cm or less. The optical member can be produced by subjecting a volatile silicon compound to flame hydrolysis with oxyhydrogen flame, depositing the formed particulate silica on a heat-resistant support to prepare a porous silica matrix, heating the matrix in a vacuum as high as 1.times.10.sup.-2 Torr or above to a temperature of 1,400 .degree. C. or above to effect dehydration and degassing, homogenizing the resultant transparent quartz glass into highly homogeneous quartz glass free from striae in at last one direction, molding the highly homogeneous quartz glass, and annealing the molded glass.