Using the non-equilibrium Green's function method combined with the density functional theory, we investigate the spin transport properties of carbon chains connected with armchair- and zigzag-edged graphene nanoribbon (ZGNR) electrodes at finite bias with the parallel magnetism configuration. When spin polarized electrons are injected into carbon chains from the ZGNR electrode, the beta-spin current is nearly zero, while the alpha-spin current shows large values in the calculated bias region, thus the spin polarization 100% can be achieved, which is a promising pathway for...