Regarding a cerium oxide-based abrasive containing cerium oxide as a main component and abrasive particles with an average particle diameter of 0.2 to 3.0 &mgr;m, the present invention provides a cerium-based abrasive containing coarse particles of 10 &mgr;m or larger in a concentration of 1000 ppm or lower (by weight) or magnetic particles in a concentration of 1000 ppm or lower (by weight). The coarse particles or the magnetic particles are particularly preferable to exist in a concentration of 300 ppm or lower (by weight). Further, by controlling an average value of the specific surface area of the abrasive particles to be within 0.5 to 30 m2/g, the resulting abrasive is provided with a high cutting property and is capable of forming a polished face with high precision. The production method of such cerium-based abrasives comprises control being the concentration of the coarse particles and the classification point and repeated classification. The control of the magnetic particle concentration is made possible by utilization of a filter of a magnetic material and alteration of pulverization media, which are either solely or properly combined with each other to be performed.