The invention relates to a cerium-based catalyst, and relates to an application of the cerium-based catalyst in methane oxyhalogenation methods used for preparing halogenated methane. The methane oxyhalogenation methods used for preparing halogenated methane comprise a methane chlorine oxidation method used for preparing methyl chloride and a methane bromine oxidation method used for preparing methyl bromide. The cerium-based catalyst is suitable to be used in methane oxyhalogenation reactions. The cerium-based catalyst can be a CeO2 catalyst, a cerium-based bi-component composite oxide catalyst, a load-type cerium-based oxide catalyst, or the like. With the cerium-based catalyst, the methane oxyhalogenation reactions including a chlorine oxidation reaction and a bromine oxidation reaction can be effectively and stably catalyzed, and methyl chloride and methyl bromide can be prepared. With the cerium-based catalyst, reactants such as CH4, HCl and O2 can be catalytically converted with high efficiency for carrying out a chlorine oxidation reaction, such that products CH3Cl and CH2Cl2 are produced. Also, with the cerium-based catalyst, reactants such as CH4, HBr(H2O), and O2 can be converted with high efficiency for carrying out a bromine oxidation reaction, such that products CH3Br and CH2Br2 are produced.