IceCube is a neutrino observatory deployed in the glacial ice at the geographic South Pole. The nu(mu) energy unfolding described in this paper is based on data taken with IceCube in its 79-string configuration. A sample of muon neutrino charged-current interactions with a purity of 99.5% was selected by means of amultivariate classification process based on machine learning. The subsequent unfolding was performed using the software TRUEE. The resulting spectrum covers an E-nu-range of more than four orders of magnitude from 125 GeV to 3.2 PeV. Compared to the Honda atmospheric neutrino flux model, the energy spectrum shows an excess of more than 1.9 sigma in four adjacent bins for neutrino energies E-nu >= 177.8 TeV. The obtained spectrum is fully compatible with previous measurements of the atmospheric neutrino flux and recent IceCube measurements of a flux of high-energy astrophysical neutrinos.