Total and partial densities of states of the atoms constituting zinc tungstate, ZnWO4, have been calculated using the ab initio full potential linearized augmented plane wave (FP-LAPW) method. The theoretical data reveal that main contributors in the valence band of ZnWO4 are the Zn 3d-, W 5d- and O 2p-like states: the Zn 3d- and W 5d-like states contribute mainly at the bottom, whilst the O 2p-like states at the top of the valence band, with also significant portions of contributions of the above states throughout the whole valence-band region of the tungstate under study. In addition, data of our band-structure FP-LAPW calculations indicate that the conduction band of ZnWO4 is dominated by contributions of the W 5d-like states. To verify the theoretical findings, high-quality inclusion-free ZnWO4 single crystals were specially grown along the  direction for the present experimental studies employing the low thermal gradient Czochralski technique. It has been established that, comparison on a common energy scale of the X-ray photoelectron valence-band spectrum and the X-ray emission bands representing the energy distribution of mainly the Zn 3d-, W 5d- and O 2p-like states of ZnWO4 confirm experimentally the present FP-LAPW theoretical data regarding the occupations of the valence band of zinc tungstate.