The supramolecular conductor (Me-3,5-DIP)[Ni(dmit)(2)](2), which was prepared by electrochemical oxidation, consists of two crystallographically independent layers of Ni(dmit)(2) anions (Layers I and II). The tight-binding band calculation suggests that Layer I is in a Mott insulating state to include localized spins, and Layer II displays two-dimensional metallic conduction. The coexistence of the two contrastive molecular pi-electrons of Ni(dmit)(2) anions is evidenced by electrical resistivity and magnetic susceptibility measurements.