We present an ab initio study of the structural, electronic, and quantum transport properties of B-N-complex edge-doped graphene nanoribbons (GNRs). We find that the B-N edge codoping is energetically a very favorable process and furthermore can achieve novel doping effects that are absent for the single B or N doping. The compensation effect between B and N is predicted to generally recover the excellent electronic transport properties of pristine GNRs. For the zigzag GNRs, however, the spatially localized B-N defect states selectively destroy the doped-side spin-polarized GNR edge currents at the valence and conduction band edges. We show that the energetically and spatially spin-polarized currents survive even in the fully ferromagnetic metallic state and heterojunction configurations. This suggests a simple yet efficient scheme to achieve effectively smooth GNR edges and graphene-based spintronic devices.