Two-dimensional (2D) materials with unique structures and diverse applications have attracted extensive interest. Here, we survey a new series of two-dimensional materials, transition metal carbon nitrogen compounds (MCNs), and investigate their physical properties based on density-functional theory (DFT). We show that 2D MCN (M = Ti, Mn, Co, Cu and Zn) monolayers are dynamically, thermodynamically and mechanically stable as evidenced by the calculated phonon dispersion, molecular dynamics simulations, and elastic properties. We find that TiCN with an in-plane stiffness of 32.64 GPa nm shows non-magnetic and semiconducting nature, and MnCN is anti-ferromagnetic in the ground state with an indirect bandgap. CoCN is ferromagnetic with half-metal characteristics. Different from the strong coupling between Co and nonmetal atoms in CoCN, the magnetic moments in antiferromagnetic CuCN and ferromagnetic ZnCN are mainly localized on the N atoms. Our study predicts a new family of 2D materials, which could be applied in nanodevices and magnetic storage devices, and provides guidance on the design of novel 2D materials.