The research and design of oxygen electrode catalysts are of great significance for achieving carbon peak and carbon neutrality goals. In this study, a comprehensive study, including detailed stability, adsorption properties, electronic characteristics, and activity center configuration of ytterbium single-atom catalysts (YbNx-gra) loaded on two-dimensional nanomaterials under acidic conditions, was conducted according to density functional theory calculations. The results indicated that with the increase of nitrogen content, the efficiency of the ytterbium single-atom oxygen electrode catalysts using nitrogen solid supports was improved. There are several good linear relationships between the adsorption free energy of intermediates, such as Delta G(OH)* and Delta G(OOH)*, Delta G(OH)*, and Delta G(O)*. This provides a basis for the drawing of volcano maps and the rapid prediction of highly active catalysts. Due to the reaction selectivity of catalysts, the O* intermediates and 2OH* intermediates accompany the catalytic reaction. For catalytic activity, the YbN4-II catalyst showed the lowest overpotential of ORR which eta(ORR) = 0.42 V. In particular, the eta(ORR) and eta(OER) of the YbN3-IV catalyst were as low as 0.58 and 0.41 V, respectively. The linear relationships and volcano plots indicate the feasibility of some YbNx-gra catalysts, making them promising candidates for oxygen electrode catalysts.