We report a study of the valence-band electronic structure of the rare-earth metal holmium. Angle-resolved ultraviolet photoemission experiments have been performed on Ho(0001) and the results compared to first-principles photocurrent calculations. The photoemission results show a number of well-resolved features that do not disperse with photon energy for h\ensuremath{\nu}g20 eV. We identify one of these features, at a binding energy of 1.7 eV, as emission from the ${\mathrm{\ensuremath{\Gamma}}}_{4\mathrm{\ensuremath{-}}}$ point of the bulk band structure. Considerable dispersion of some of these features with emission angle has enabled us to map, in detail, the experimental bands of the (0001) surface along the \ensuremath{\Gamma}M and \ensuremath{\Gamma}KM symmetry directions. Comparison of the experimental spectra with photocurrent calculations employing a realistic potential in the surface layers suggests that the remaining features are due to surface effects. The binding energy of one of the calculated peaks is higher by 0.9\ifmmode\pm\else\textpm\fi{}0.05 eV than that seen in experiment and possible reasons for this discrepancy are discussed.