The polishing composition contains an abrasive, a microwaviness reducing agent, an oxidizing agent, a polishing accelerator, and water. The microwaviness reducing agent is a reducing agent and contains at least one kind selected from phosphonic acid, phosphinic acid, ammonium hypophosphite, ammonium sulfite, sodium sulfite, hydroquinone, pyrogallol, erysorbic acid, sodium erysorbate acid, L-ascorbic acid, formic acid, sodium formate, amumonium formate, oxalic acid, ammonium oxalate, ammonium iodide, and gallic acid. The abrasive can contain silicon dioxide, and the oxidizing agent can contain hydrogen peroxide. The accelerator can contain e.g. phosphoric acid, glycolic acid, maleic acid or succinic acid as well as diammonium hydrogen phosphate or ammonium dilhydrogen phosphate. The polishing composition can be used in polishing a substrate for a magnetic disk.