We perform density functional calculations on one-dimensional zigzag edge graphene nanoribbons (ZGNRs) of different widths, with and without edge doping including semilocal exchange correlations. Our study reveals that, although the ground state of edge-passivated (with hydrogen) ZGNRs prefers to be anti-ferromagnetic, the doping of both of the edges with boron atoms stabilizes the system in a ferromagnetic ground state. Both the local and semilocal exchange correlations result in half-metallicity in edge-passivated ZGNRs at a finite cross-ribbon electric field. However, the ZGNR with boron edges shows half-metallic behavior irrespective of the ribbon width even in the absence of electric field and this property sustains for any field strength, opening a huge possibility of applications in spintronics.