To polish polishing target surfaces of SiO.sub.2 insulating films or the like at a high rate without scratching the surface, the present invention provides an abrasive comprising a slurry comprising a medium and dispersed therein at least one of i) cerium oxide particles constituted of at least two crystallites and having crystal grain boundaries or having a bulk density of not higher than 6.5 g/cm.sup.3 and ii) abrasive grains having pores. Also provided are a method of polishing a target member and a process for producing a semiconductor device which make use of this abrasive.