Alkaline-earth metal oxides with the rocksalt structure, which are simple ionic solids, have attracted attention in attempts to gain fundamental insights into the properties of metal oxides. The surfaces of alkaline-earth metal oxides are considered promising catalysts for the oxidative coupling of methane (OCM); however, the development of such catalysts remains a central research topic. In this paper, we performed first-principles calculations to investigate the ability of four alkaline-earth metal oxides (MgO, CaO, SrO, and BaO) to catalyze the OCM. We adopted five types of surfaces of rocksalt phases as research targets: the (100), (110), stepped (100), oxygen-terminated octopolar (111), and metal-terminated octopolar (111) surfaces. We found that the formation energy of surface O vacancies is a good descriptor for the adsorption energy of a H atom and a methyl radical. The energies related to the OCM mechanism show that, compared with the most stable surface, the minor surfaces better promote the C - H bond cleavage of methane. However, as the trade-off for this advantage, the minor surfaces exhibit increased affinity for the methyl radical. On the basis of this trade-off relationship between properties, we identified several surfaces that we expect to be promising OCM catalysts. Our investigation of the temperature dependence of the Gibbs free energy indicated that, at higher temperatures, the step (100) surface exhibits properties that might benefit the OCM mechanism.