To efficiently polish a substrate by using a higher load, by making improvement to make large polishing resistance at the time of polishing a large-sized substrate smaller.

In this method for manufacturing the substrate 4 for a mask blank, there is provided a process for relatively moving a surface plate 1 bonded to polishing cloth 2 and the substrate 4 for the mask blank in a fixed load applied state, supplying polishing liquid between contact surfaces of the polishing cloth 2 and the substrate 4 at that time, and polishing the substrate 4. The surface plate 1 has a groove on a polishing cloth 2 bonding surface of the surface plate 1. A cross-sectional shape of the groove is constituted of: the polishing plate 1 formed into a curve shape or a curved surface shape at least an opening peripheral edge part of the groove; and the polishing cloth 2 bonded along the form of the groove having a polishing cloth bonding plane of the polishing plate 1 and the prescribed opening peripheral edge part form. By using the "prescribed surface plate bonded to the polishing cloth" 3, the substrate 4 is polished.