By using nonequilibrium Green's functions in combination with the density functional theory, the transport properties of a carbon chain-based spintronic device are investigated. Previous reports show that when the carbon chains are sandwiched between metal electrodes or perfect zigzag graphene nanoribbons, the conductance of odd-n carbon chain systems is higher than that of even-n ones [Phys. Rev. Lett., 1998, 81, 3515;J. Am. Chem. Soc., 2010, 132, 11481-11486]. However, when the carbon chains are connected with Fe-porphyrin-like armchair graphene nanoribbons, we find that low conductance stat...