The molecular and electronic structures and electron transport characteristics of a Co complex are investigated using first principles calculations. The Co complex belongs to the D-2d point group, and its two ligands are perpendicular to each other. The central atom Co forms a distorted octahedron with six donor N atoms. In a low oxidation state, the bond length between Co and pyrrole nitrogen, 1.849 angstrom, is much shorter than the distance between Co and pyridine nitrogen, 2.168 angstrom, while, in a high oxidation state, the bond length differences between Co and pyrrole nitrogen, 1.814 angstrom, and between Co and pyridine nitrogen, 1.990 angstrom, are not as large as those in the Co2+ complex. The HOMO energy of the low oxidation state is very close to the Fermi level of bulk Au, allowing hole creation in the molecule. On the other hand, the LUMO energy of the high oxidation state is close to the Au Fermi level, allowing a low barrier for electron injection from the Au cathode to the molecule. These structural characteristics make the Co complex a good hole-conduction molecule. The density of states, transmission probability, and I-V characteristics are evaluated using the Green function approach.