N-graphdiyne monolayers, a set of carbon nitride nanosheets, have been synthesized recently through the polymerization of triazine- and pyrazine-based monomers. Because the two-dimensional nanostructures are mainly composed of lightweight nonmetallic elements including carbon and nitrogen, they might be able to provide high storage capacities for rechargeable cells. In this study, we used extensive first-principles calculations such as electronic density of states, band structure, adsorption energy, open-circuit voltage, nudged-elastic band, and charge analyses to investigate the application of the newly fabricated N-graphdiyne monolayers as the anode material for Li/Na/Mg ion batteries. Our calculations suggest that while Mg foreign atoms poorly interact with monolayers, Li and Na adatoms illustrate outstanding anodic characteristics for rechargeable storage cells. Electronic density of states calculations indicate that the insertion of Li/Na into the novel N-graphdiyne materials enhances the electrical conductivity of nanosheets. Adsorption energy and open-circuit voltage calculations predict that the nanosheets can provide a high storage capacity spectrum of 623–2180 mAh/g, which is higher than that for most recently discovered 2D materials (e.g., phosphorene, borophane, and germanene involve Li binding capacities of 433, 504, and 369 mAh/g, respectively), and it is also significantly greater than the capacity of commercial anode materials (e.g., graphite contains a capacity of 372 mAh/g). This study provides valuable insights into the electronic characteristics of newly fabricated N-graphdiyne nanomaterials, rendering them as promising candidates to be used in the growing industry of rechargeable storage devices.