Two paradigm shifts in DNA sequencing technologies--from bulk to single molecules and from optical to electrical detection--are expected to realize label-free, low-cost DNA sequencing that does not require PCR amplification. It will lead to development of high-throughput third-generation sequencing technologies for personalized medicine. Although nanopore devices have been proposed as third-generation DNA-sequencing devices, a significant milestone in these technologies has been attained by demonstrating a novel technique for resequencing DNA using electrical signals. Here we report single-molecule electrical resequencing of DNA and RNA using a hybrid method of identifying single-base molecules via tunneling currents and random sequencing. Our method reads sequences of nine types of DNA oligomers. The complete sequence of 5'-UGAGGUA-3' from the let-7 microRNA family was also identified by creating a composite of overlapping fragment sequences, which was randomly determined using tunneling current conducted by single-base molecules as they passed between a pair of nanoelectrodes.