A polishing composition includes fumed alumina, alumina other than fumed alumina, colloidal silica, a first organic acid, a second organic acid, an oxidizing agent, and water. When the second organic acid is citric acid, the first organic acid is preferably malic acid, while when the second organic acid is malic acid, the first organic acid is preferably citric acid. When the second organic acid is succinic acid, iminodiacetic acid, itaconic acid, maleic acid, malonic acid, crotonic acid, gluconic acid, glycolic acid, lactic acid, or mandelic acid, the first organic acid is preferably either citric acid or malic acid. The polishing composition can be suitably used for polishing the surface of a substrate for a magnetic disk.