Cerium-based abrasive and number bath method

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There is provided a cerium-based abrasive that achieves a high polishing rate and suppresses the occurrence of surface defects such as scratches and pits and the deposition of the abrasive particles on the polished surface in surface polishing of glass substrates or the like, at low cost with a high production efficiency, and also a manufacturing method thereof. The cerium-based abrasive comprises a cubic composite rare earth oxide and a composite rare earth oxyfluoride, containing 95.0 to 99.5 mass% of total rare earth elements in terms of oxides, containing 54.5 to 95.0 mass% of cerium in terms of oxide, 4.5 to 45.0 mass% of lanthanum in terms of oxide, and 0.5 to 2.0 mass% of neodymium in terms of oxide relative to the total rare earth elements in terms of oxides, containing 0.5 to 4.0 mass% of fluorine atoms, and containing 0.001 to 0.50 mass% of sodium atoms relative to the total rare earth elements in terms of oxides and a manufacturing method thereof.