Fused silica glass having an internal transmittance of UV with 245 nm wavelength, being at least 95% at 10 mm thickness, a OH content of not larger than 5 ppm, and a content of Li, Na, K, Mg, Ca and Cu each being smaller than 0.1 ppm. Preferably the glass has a viscosity coefficient at 1215° C. of at least 1011.5 Pa·s; and a Cu ion diffusion coefficient of not larger than 1×10−10 cm2/sec in a depth range of greater than 20 μm up to 100 μm, from the surface, when leaving to stand at 1050° C. in air for 24 hours. The glass is made by cristobalitizing powdery silica raw material; then, fusing the cristobalitized silica material in a non-reducing atmosphere. The glass exhibits a high transmittance of ultraviolet, visible and infrared rays, has high purity and heat resistance, and exhibits a reduced diffusion rate of metal impurities, therefore, it is suitable for various optical goods, semiconductor-production apparatus members, and liquid crystal display production apparatus members.