The discovery of graphene makes it highly desirable to seek new two-dimensional materials. Through first-principles investigation, we predict two-dimensional materials of ReN$_{2}$: honeycomb and tetragonal structures. The phonon spectra establish the dynamical stability for both of the two structures, and the calculated in-plane stiffness constants proves their mechanical stability. The energy bands near the Fermi level consist of N-p and Re-d orbitals for the honeycomb structure, and are mainly from Re d orbitals for the tetragonal structure. While the tetragonal structure is non-magnetic, the honeycomb structure has N-based ferromagnetism, which will transit to anti-ferromagnetism under 14$%$ biaxial strain. The calculated electron localization function and spin density indicate that direct N-N bond can occur only in the honeycomb structure. The ferromagnetism allows us to distinguish the two 2D phases easily. The tetragonal phase has lower energy than the honeycomb one, which means that the tetragonal phase is more stable, but the hexagonal phase has much larger bulk, shear, and Youngs muduli than the tetragonal phase. The tetragonal phase is a three-bands metal, and the hexagonal phase is a ferromagnetic semi-metal. The special structural, electronic, magnetic, and optical properties in the honeycomb and tetragonal structures make them promising for novel applications.
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