We investigate electronic structures and transport properties of chiral-graphene-nanoribbons (CGNRs) with reconstructed (2,1)-edges. First principles results reveal that the (2,1)-CGNRs can be either spin non-polarized or polarized, depending on whether the edges are H-saturated or unsaturated. H-saturated systems are semiconductors with width-dependent transmission gap, while unsaturated systems are metallic at non-polarized state or at antiferromagnetic state and they are semiconductors at ferromagnetic state. Moreover, unsaturated systems possess strong current polarizations (nearly 100%) and a striking negative differential resistance behavior (with a peak-to-valley ratio about 105). These remarkable properties suggest the potential application of (2,1)-CGNRs in molectronics and spintronics.