A glass-substrate manufacturing method according to an aspect of the invention is a method for manufacturing glass substrates by employing a down-draw process. In down-draw processing, a molten glass is made to overflow from a forming member and formed into a sheet glass and the sheet glass is then cooled while being drawn in a downward-flow direction. In this glass-substrate manufacturing method, after the sheet glass has separated from the forming member and when the temperature of the sheet glass is within a temperature region ranging from a temperature higher than the softening point to a temperature near the annealing point, the sheet glass is cooled by maintaining the viscosity of side sections of the sheet glass within a range of 109.0-1014.5 poise while applying a tension toward the side sections.