The electronic structure of the hexagonal-closed-packed elements Be, Mg, Sc, Ti, Co, Zn, Y, Zr, Tc, Ru, and Cd is calculated self-consistently by means of the full potential linearized augmented-plane-wave method. Energy-band structures, total and partial densities of states, as well as electron densities are presented and discussed in context with available experimental and theoretical data. Our results confirm that most of the older non-self-consistent calculations obtained realistic energy-band structures, while calculations based on the quantum-defect method generally yield completely different results.