Partial oxidation of methane has been conducted over $CeO_2$and it has been found that $CeO_2$has an extraordinary catalytic activity in the reaction. Its activity was strongly dependent on the $CH_4/CO_2$ ratio. Total combustion was dominant with stoichiometric feed ratio$(CH_4/O_2=$ 2.0) but partial oxidation was achieved between the $CH_4/O_2$ ration of 3.8 4.3 and the period depended upon the feed composition. The proposed raaction mechanism it that oxygen vacancies in raduced deria are supplied with oxygen molecules from the reactant, and then activate adsorbed oxygen, followed by releasing activated axygen species reacting with methane to produce $H_2$ and CO.