Using first-principles calculations based on density functional theory (DFT) and nonequilibrium Green's function method, we systematically investigated the electronic and magnetic structures, local structural distortion, and electronic spin transport property of a zigzag silicon carbide nanoribbon (ZSiC NR) containing one isolated nonmagnetic impurity [boron (B) or nitrogen (N)] at the inequivalent substitutional sites. Our calculated results reveal that by controlling the doping position without an applied electronic field, greatly enriched electronic and magnetic properties, e.g., semiconducting, half-metallic, and metallic behaviors, as well as the ferrimagnetic–ferromagnetic conversion, can be achieved in both B- and N-doped ZSiC NRs. Interestingly, all the doped ZSiC NRs of B substituting Si atom and N substituting C atom have 100% spin transport polarization around the Fermi level and exhibit spin filtering behavior. It is found that except for position at the edge C-site, the boron at other sites suppresses the local magnetic moment at edge Si atoms and enhances the local magnetic moment at edge C atoms. On the contrary, except for position at the edge Si-site and its nearest-neighbor Si-site, the nitrogen at other sites suppresses the local magnetic moment at edge C atoms and enhances the local magnetic moment at edge Si atoms. It is also found that when the impurity atom substitutes Si atom, visible local structural distortion occurs around the impurity atom, whereas when the impurity atom substitutes C atom, only a minor local structural distortion occurs. Additionally, the local structural distortion around impurity atom becomes more pronounced when the impurity moves from the edge toward the center. These doping effects are discussed by using the band structures, projected density of states (DOS), electronegativity, as well as Mulliken charge analysis.