A nonlocal semiempirical pseudopotential calculation of the electronic structure of wurtzite ZnO is proposed. The local and nonlocal components of the atomic effective potentials have been sequentially optimized and an excellent quantitative agreement has been achieved with a wide range of band features (energy gaps at high symmetry points, valence band ordering, in-plane and perpendicular components of the effective masses for electrons and holes at Gamma), selected not only from available experimental and ab initio results, but also from new calculations performed with the code developed by the ABINIT project. The valence band description has been further improved through the inclusion of spin-orbit corrections. The complex dielectric function along the main crystallographic directions corresponding to the optimized electronic structure is also presented, along with extensive comparisons of all the computed quantities with the literature data.