Based on first-principles calculations, we predict a class of graphene-like magnetic materials, transition metal carbonitrides MN4C6 (M = Cr, Mn, Fe, and Co), which are made up of a benzene ring and an MN4 moiety, two common planar units in the compounds. The structural stability is demonstrated by the phonon and molecular dynamics calculations, and the formation mechanism of the planar geometry of MN4C6 is ascribed to the synergistic effect of sp2 hybridization, M-N coordination bond, and π-d conjugation. The MN4C6 materials consist of only one layer of atoms and the transition metal atom is located in the planar crystal field, which is markedly different from most two-dimensional materials. The calculations indicate that MnN4C6, FeN4C6, and CoN4C6 are ferromagnetic while CrN4C6 has an antiferromagnetic ground state. The Curie temperatures are estimated by solving the anisotropic Heisenberg model with the Monte Carlo method.