A full-potential band structure calculation, within the density functional theory and the local density approximation, has been performed for the hexagonal close-packed polytypes 2H, 4H and 6H of Si. Calculated lattice constants are found to be in good agreement with experimental values. Energy band gap, crystal-field splitting and spin-orbit splitting have been determined and, furthermore, the effective masses have been calculated for the lowest conduction band and the two uppermost valence bands. Throughout the paper, comparison is made with corresponding polytypes of SiC and with diamond cubic Si.