A method for producing a high-purity, white opaque quartz glass containing 3.times.10.sup.6 -9.times.10.sup.6 of closed cells having an average size of 20-40 .mu.m per 1 cm.sup.3, a ratio of closed cells having sizes of 100 .mu.m or more to the whole of cells being 1% or less, thereby showing 5% or less of linear transmittance for near infrared rays, having a .lambda.=900 nm, at a thickness of 1 mm, said method comprising the steps of compacting amorphous silica powder having an average particle size of 0.5-10 .mu.m, each of impurities selected from Li, Na, K, Fe, Ti and Al being 1 ppm or less, heating the resultant green body to 1750.degree.-1850.degree. C. at a heating speed of 300.degree.-600.degree. C. per 1 hour, and sintering the green body at 1750.degree.-1850.degree. C. and at a pressure of 1-2 kgf/cm.sup.2 in an atmosphere selected from the group consisting of N.sub.2, O.sub.2, Ar and a mixture thereof.