We investigated theoretically how molecular conjugation affects current-voltage (I-V) curves through three types of oligoporphyrin molecules, i.e., the tape-porphyrin, the butadiyne-linked porphyrin, and the edge-fused porphyrin molecules. Among these, the tape-porphyrin molecule is found to be the most conductive due to its extremely small HOMO-LUMO energy gap. Furthermore, the I-V curves through this type of molecule are found to depend considerably on atomic sites to which electrodes are connected. In particular, as long as the applied bias is weak, the current is found to flow strongest when both electrodes are connected to the atomic sites referred to as meso sites. This feature is caused by the fact that the HOMO relevant to resonant tunneling has a higher charge density on the meso sites. These findings indicate that designing not only molecules but also contact structures is highly significant for realizing a desirable function in single molecular devices. (C) 2004 Elsevier B.V. All rights reserved.