To provide a polishing composition capable of increasing polishing rate and reducing surface roughness, without causing surface defects on a surface of an object to be polished; and a polishing process for a substrate to be polished. [1] a polishing composition comprising water, an abrasive, an intermediate alumina, and a polycarboxylic acid having 4 or more carbon atoms with no OH groups or a salt thereof, wherein a content of the intermediate alumina is from 1 to 90 parts by weight, based on 100 parts by weight of the abrasive; and [2] a polishing process for a substrate to be polished, comprising polishing a substrate to be polished under conditions that a composition of a polishing liquid during polishing is the composition as defined in item [1] above.