On an EUV light-reflecting surface of titania-doped quartz glass, an angle (θ) included between a straight line connecting an origin (O) at the center of the reflecting surface to a birefringence measurement point (A) and a fast axis of birefringence at the measurement point (A) has an average value of more than 45 degrees. Since fast axes of birefringence are distributed in a concentric fashion, a titania-doped quartz glass substrate having a high flatness is obtainable which is suited for use in the EUV lithography.