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Variable-range hopping is usually the main electron transport mechanism of an organic semiconductor at low temperature. For an organic field-effect transistor at low temperature and under both high source-drain bias and high gate voltage, it is argued that multistep tunneling (MUST) can dominate charge transport. The MUST occurs through the assistance of randomly distributed localized states. The conductivity depends exponentially on the inverse of the square-root of electric field. This result explains well the recent experimental observation [A. S. Dhoot etal, Phys. Rev. Lett. 96, 246403 (2006)].