The structure and stability of the two-dimensional methane hydrate confined within two graphene sheets are examined with density functional theory. Our calculations suggest that the confined methane hydrate has two distinct patterns, namely, the stable "plum-pudding" structure and the less stable "sandwich" structure. Further, our results indicate that the initial formation process of two-dimensional methane hydrate is that water molecules arrange around the methane molecule to create tetragonal rings that are vertical to the graphene sheet, which will further result in the formation of an intact cage.