We studied charge transport through core-substituted naphthalenediimide (NDI) single-molecule junctions using the electrochemical STM-based break-junction technique in combination with DFT calculations. Conductance switching among three well-defined states was demonstrated by electrochemically controlling the redox state of the pendent diimide unit of the molecule in an ionic liquid. The electrical conductances of the dianion and neutral states differ by more than one order of magnitude. The potential-dependence of the charge-transport characteristics of the NDI molecules was confirmed by DFT calculations, which account for electrochemical double-layer effects on the conductance of the NDI junctions. This study suggests that integration of a pendant redox unit with strong coupling to a molecular backbone enables the tuning of charge transport through single-molecule devices by controlling their redox states.