Rapid sequencing of individual human genome is prerequisite to genomic medicine, where diseases will be prevented by preemptive cures. Quantum-mechanical tunneling through single-stranded DNA in a solid-state nanopore has been proposed for rapid DNA sequencing, but unfortunately the tunneling current alone cannot distinguish the four nucleotides due to large fluctuations in molecular conformation and solvent. Here, we propose a machine-learning approach applied to the tunneling current-voltage (I-V) characteristic for efficient discrimination between the four nucleotides. We first combine principal component analysis (PCA) and fuzzy c-means (FCM) clustering to learn the "fingerprints" of the electronic density-of-states (DOS) of the four nucleotides, which can be derived from the I-V data. We then apply the hidden Markov model and the Viterbi algorithm to sequence a time series of DOS data (i.e., to solve the sequencing problem). Numerical experiments show that the PCA-FCM approach can classify unlabeled DOS data with 91% accuracy. Furthermore, the classification is found to be robust against moderate levels of noise, i.e., 70% accuracy is retained with a signal-to-noise ratio of 26 dB. The PCA-FCM-Viterbi approach provides a 4-fold increase in accuracy for the sequencing problem compared with PCA alone. In conjunction with recent developments in nanotechnology, this machine-learning method may pave the way to the much-awaited rapid, low-cost genome sequencer.