There is provided an abrasive used for polishing a substrate which comprises silica as a main component, for example a rock crystal, a quartz glass for photomask, for CMP of an organic film, Inter Layer Dielectric (ILD) and shallow trench isolation of a semiconductor device, or for polishing a hard disk made of glass. A sol which particles are dispersed in a medium, wherein the particles have a particle size of 0.005 to 1 µm and comprise as a main component crystalline cerium oxide of the cubic system and as an additional component a lanthanum compound, a neodymium compound or a combination thereof, wherein the additional component is contained in X/(Ce + X) molar ratio of 0.001 to 0.5 in which X is lanthanum atoms, neodymium atoms or a combination thereof. The sol is prepared by reacting an aqueous solution which a cerium (III) salt is mixed with a lanthanum (III) salt and/or a neodymium (III) salt, with an alkaline substance to give a suspension in which cerium (III) hydroxide is homogeneously mixed with lanthanum (III) hydroxide and/or neodymium (III) hydroxide, and blowing oxygen or a gas containing oxygen into the suspension.