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A cerium-based abrasive material which inhibits polishing scratches from generating and attains a significantly improved polishing rate. The cerium-based abrasive material has a cerium oxide content of 95 mass% or higher based on the total rare-earth oxides (TREO), and is characterized in that the particle diameter (D50) corresponding to the cumulative volume of 50% from the small-particle-diameter side in examination by the laser diffraction/scattering method is 1.3-4.0 µm. When analyzed by X-ray diffractometry with a Cu-Kα1 line, the cerium-based abrasive material preferably is one in which the maximum peak for cerium oxide has a half band width of 0.1-0.5° in terms of 2θ.