The present invention relates to a polishing composition containing a colloidal silica prepared from a silicate, the colloidal silica having an average particle size of primary particles of 1 nm or more and less than 40 nm, and water, wherein a density of silanol group on the surface of the colloidal silica is from 0.06 to 0.3 mmol per 1 g of the colloidal silica; a process for preparing the abovepolishing composition; a method for reducing nano scratches of a substrate and a method for manufacturing a substrate, each including the step of polishing a substrate to be polished with a polishingcomposition comprising a colloidal silica prepared from a silicate, the colloidal silica having an average particle size of primary particles of 1 nm or more and less than 40 nm, and water, wherein adensity of silanol group on the surface of the colloidal silica is adjusted to a range from 0.06 to 0.3 mmol per 1 g of the colloidal silica. The polishing composition is suitable for polishing substrates for precision parts including, for instance, substrates for magnetic recording media, such as magnetic disks, optical disks, and opto-magnetic disks, photomask substrates, optical lenses, optical mirrors, optical prisms and semiconductor substrates, and the like.