First principles calculations are performed to study the spin polarized transport in zigzag-edged graphene nanoribbons with anti-ferromagnetic ordering. It is found that when a single B or an N atom is doped in the central scattering region, their effects on the different spin components of current are completely different, though they play the same role in reducing the magnetic moments of the edge carbon atoms. In the B doping case, the spin-up component in current is much larger than the spin-down component, while the situation is opposite to the N doping case. This originates from the fact that the spin degeneracy is broken and the spin-up energy levels in the valence band and the conduction band are higher than the spin-down energy levels in both cases. B doping introduces a hole so that the fully filled valence band becomes partially filled and the Fermi level shifts down to the spin-up energy levels in the valence band while the spin-down energy levels in it are a little far from the Fermi level. This strengthens the transmission of electrons in the spin-up channel more than it does for the spin-down electrons. N doping introduces an electron which makes the empty conduction band partially filled so that the Fermi level shifts up to the spin-down energy levels in the conduction band. This strengthens the transmission of electrons in the spin-down channel more than it does for the spin-up electrons.