A polishing composition capable of satisfactorily polishing a semiconductor. The first polishing composition of the present invention includes silicon dioxide, at least one component selected from periodic acids and salts thereof, at least one component selected from tetraalkyl ammonium hydroxides and tetraalkyl ammonium chlorides, hydrochloric acid, and water, and contains substantially no iron. The second polishing composition of the present invention includes a predetermined amount of fumed silica, a predetermined amount of at least one component selected from periodic acids and salts thereof, a tetraalkyl ammonium salt represented by the following general formula (1), at least one component selected from ethylene glycol and propylene glycol, and water. The pH of the second polishing composition is greater than or equal to 1.8 and is less than 4.0. ##STR00001##