The hydrogen-passivated N chains zigzag silicon carbide nanoribbons (N-ZSiC NRs) are indexed by its width N (the number of zigzag Si–C chains across the nanoribbon). Using density-functional theory (DFT) with the Heyd–Scuseria–Ernzerh screened hybrid functional (HSE06) and the Perdew–Burke–Ernzerhof functional (PBE), we investigate the edge energy and electronic and magnetic properties of the ultra-narrow N-ZSiC NRs (2 6). Our calculated results reveal effects of short-range exact exchange on the edge energy, the band gap, and the magnetic properties of the ultra-narrow N-ZSiC NRs. It is noted that the inclusion of a portion of short-range exact exchange enhances the calculated band gap. HSE06 functional calculations confirm that the ultra-narrow N-ZSiC NRs (4 6) are ferrimagnetic semiconductors, and the 2-ZSiC and 3-ZSiC NRs are nonmagnetic semiconductors. Moreover, the calculated local magnetic moments at the edge carbon and silicon atoms (those connected to hydrogen). It is also found that the inclusion of a portion of short-range exact exchange always lower the calculated edge energy of the ultra-narrow N-ZSiC NRs. As a comparison we also used the HSE06 functional as well as the PBE functional to investigate the edge energy, as well as electronic and magnetic properties, of the hydrogen-passivated N chains zigzag graphene nanoribbon (N-ZG NRs, 2 4). It is noted that the short-range exact exchange corrections to the edge energy, band gap, and edge atom's local magnetic moment are more striking in the ultra-narrow N-ZG NRs than in the ultra-narrow N-ZSiC NRs. At lastly, we present the origin why when 3, the N-ZSiC NR has only a NM state, while all N-ZG NRs have AFM states.