Continuous ZnO thin films have been grown at low temperature (400 degrees C) on GaN/c-sapphire substrates in a radio-frequency magnetron-sputtering chamber employing a substoichiometric ZnO target with and without extra oxygen feeding. The effects of oxygen on the growth and band alignment of the ZnO/GaN heterostructures were investigated by using scanning-electron microscopy, x-ray diffraction, photoluminescence and transmittance/absorbance, ultraviolet-resonant Raman scattering, and x-ray photoelectron spectroscopy. Very remarkable changes of the structural and optical properties resulted from the introduction of oxygen: the surface hexahedral facets were diminished; the size of the surface islands and, hence, the compressive strains were reduced; ultraviolet transparency of the ZnO film was enhanced, together with an increased band gap due to the reduced intrinsic shallow-donor defects; and hence, the free-electron concentration. The offset in valence bands of the ZnO/GaN heterostructure was increased by similar to 90 meV at certain conditions. This is likely due to the increased Ga-O bonds at the ZnO/GaN interface by the incorporation of extra oxygen at the initial growth of ZnO.