Recently, molecular electronics has become increasingly important. By applying the hybrid density functional theory coupled with the Green's function method, the current-voltage characteristics of the molecular junctions composed of gold-porphyrin-gold and gold-copper porphyrin-gold were investigated. The role of the metal coordination effect in organic molecular electron transport was highlighted. Although the thresholds of the bias voltage for both molecules were almost the same, approximately 0.9 V, the metal compound showed a larger increase in current because of the metal-coordination-enhanced molecule-electrode coupling in the frontier molecular orbitals.