Density-functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the transport code SMEAGOL and applied to the prototypical case of benzene molecules and gold electrodes. The Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low-bias current in much better agreement with experiments.
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