Nuclear magnetic resonance H-1, O-16, and O-17 chemical shifts, as well as O-17 quadrupolar parameters in several isomers of water hexamer clusters, are studied using density functional theory calculations and the gauge including projector augmented wave (GIPAW) pseudopotential method. The prism, cage, book, bag, chain, and two cyclic isomers are investigated, and structures with O-16 and O-17 nuclei are examined. It is found that the hydrogen and oxygen chemical shifts show a substantial variation. In six more stable hexamers, all quadrupole coupling Constants decrease and asymmetry parameters increase in a comparison with bulk water, whereas a chain isomer shows an opposite behavior. The values of NMR parameters are in reasonable agreement with existing results obtained by more computationally demanding methods.