A polishing composition is provided containing an abrasive having an average particle size of from 1 to 30 nm and water, wherein the abrasive has a packing ratio of from 79 to 90% by weight; a method for manufacturing a substrate, including the steps of introducing the above polishing composition between a substrate and a polishing pad, and polishing the substrate, while contacting the substrate with the polishing composition; and a method for reducing scratches of a substrate to be polished, including the step of polishing the substrate to be polished with the above polishing composition. The polishing composition is suitable for polishing substrates for precision parts including, for example, substrates for magnetic recording media, such as magnetic disks, and opto-magnetic disks, photomask substrates, optical disks, optical lenses, optical mirrors, optical prisms and semiconductor substrates, and the like.