A polishing composition comprising a colloidal dispersion of spherical silica particles and associated silica particles as abrasive is provided. When used in the step of polishing synthetic quartz glass substrates, the polishing composition ensures a higher polishing rate than conventional colloidal silica and is effective for preventing any microscopic defects on the substrate surface, thus providing the substrate with a high smoothness. The polishing composition can be used as the ceria replacement polishing composition for polishing a lapped surface.