The spin-related transport properties of graphene nanoribbons with zigzag edges which are partially coupled to Au linear-chain electrodes have been investigated by using non-equilibrium Green’s function in combination with the density-functional theory. The results show that the partial contact with the electrodes will break the spin degeneracy, leading to the completely spin-polarized transport. Meanwhile, the spin-related properties are obviously dependent on the electrodes contact positions. For the boron doped graphene nanoribbons, the spin polarized effect is enhanced.