We studied the electronic structure of cobalt-phthalocyanine (CoPc) molecules on an Au(111) surface by scanning tunneling microscopy and spectroscopy at 5K. The differential conductance (dI=dV) spectrum measured on the Co atom showed a peak related to the d orbital of the Co atom, whereas that measured on the Pc ring showed three peaks related to the highest occupied molecular orbital ( HOMO), HOMO-1 and the lowest unoccupied MO (LUMO). The current-voltage characteristics showed dependence on the position measured within the molecule, indicating that the intramolecular position of the contact between the molecule and the electrode made influence on carrier transport through a single molecule.