Density functional theory studies of the structural and electronic properties of nanoclusters (ZnO)n (n = 34, 60) in different geometric configurations were conducted. For each cluster, an optimization (relaxation) of structure geometry was performed, and the basic properties of the band structure were investigated. It was established that for the (ZnO)34 nanoclusters, the most stable are fullerene-like hollow structures that satisfy the rule of six isolated quadrangles. For the (ZnO)60 nanoclusters, different types of isomers, including hollow structures and sodalite-like structures composed from (ZnO)12 nanoclusters, were investigated. It was determined that the most energetically favorable structure was sodalite-type structure composed of seven (ZnO)12 clusters with common quadrangle edges.