A polishing composition comprising a chelating compound or a salt thereof; a partially esterified product and/or partially etherified product of a polyhydric alcohol compound; and water; a polishing composition comprising water, an abrasive, an intermediate alumina, and a chelating compound or a salt thereof, wherein the content of the intermediate alumina is from 1 to 50 parts by weight, based on 100 parts by weight of the abrasive; and a polishing composition comprising water, an abrasive, an intermediate alumina, a chelating compound or a salt thereof, and a partially esterified product and/or partially etherified product of a polyhydric alcohol compound, wherein the content of the intermediate alumina is from 1 to 50 parts by weight, based on 100 parts by weight of the abrasive. By using the polishing composition, the polishing rate can be increased, and the surface roughness can be lowered, without causing defects such as scratches and pits on the surface of an object to be polished.