A process for producing a glass substrate for information recording media, comprising lapping a glass disk made of low alkali aluminosilicate glass that contains no alkali metal oxide or contains alkali metal oxides in a total amount of less than 4 mol %, and subsequently polishing the glass disk by using a slurry that contains cerium oxide abrasives, characterized by cleaning the glass disk by using a cleaning liquid that contains sulfuric acid at a concentration of from 20 mass % to 80 mass % and hydrogen peroxide at a concentration of from 0.5 mass % to 10 mass % at a liquid temperature of from 50° C. to 100° C., and thereafter polishing the main surface of the glass disk, by using a slurry that contains colloidal silica abrasives.