Two-dimensional carbon nitride (2DCN) materials have emerged as an important class of 2D materials beyond graphene. However, 2DCN materials with nodal-line semimetal characteristic are rarely reported. In this work, a new nodal-line semimetal 2DCN with the stoichiometry CN is designed by using density functional theory (DFT) calculations and its application to anchor single-atom catalysts (SACs) for the oxygen reduction reaction (ORR) is investigated. CN is a planar covalent network (sp hybridization) with regular holes formed by the four N atoms, which is dynamically, thermodynamically, and mechanically stable. The nodal line is contributed by the p orbitals of C and p orbitals of N atoms. CN shows an anisotropic Fermi velocity and high electron mobility. Because of its porous structure, CN can anchor heteroatoms as SACs for electrocatalysis. CN anchored with Fe or Co is shown to be highly active for the ORR with a rather high half-wave potential of around 0.90 V, which is higher than those of SACs on other carbon nitrides. These findings may provide a new strategy to design novel substrates for SACs.