A polishing composition of the present invention contains silicon dioxide, an acid, and water. Silicon dioxide is, for example, colloidal silica, fumed silica, or precipitated silica. The acid is, for example, hydrochloric acid, phosphoric acid, sulfuric acid, phosphonic acid, nitric acid, phosphinic acid, boric acid, acetic acid, itaconic acid, succinic acid, tartaric acid, citric acid, maleic acid, glycolic acid, malonic acid, methanesulfonic acid, formic acid, malic acid, gluconic acid, alanine, glycin, lactic acid, hydroxyethylidene diphosphonic acid, nitrilotris(methylene phosphonic acid), or phosphonobutane tricarboxylic acid. The pH of the polishing composition is preferably in the range of 0.5 to 6. The polishing composition can be suitably used in applications for polishing a glass substrate.