There is provided a process for smoothing a substrate surface having a concave defect, such as a pit or a scratch. A process for smoothing a surface of a glass substrate for a reflective mask blank used in EUV lithography, comprising disposing a thin film on a glass substrate; detecting a concave defect existing on the glass substrate; and locally heating or locally anodizing a portion of the thin film just above the detected concave defect to perform a chemical reaction accompanied by a volume increase in a material forming the thin film.