With pulsed laser deposition, the Cu0.04Zn0.96O thin films are grown at 600 °C under three different oxygen pressures, namely PO2 = 0.00, 0.02, and 1.00 Pa. X-ray diffraction shows single-phase material for the samples grown under PO2 = 0.00 and 1.00 Pa and CuO secondary phase for the PO2 = 0.02 Pa grown sample. The observation of satellite structures in the Cu 2p core level X-ray photoelectron spectroscopy (XPS) spectra suggest the presence of Cu2+ and CuO secondary phases in the samples grown at PO2 = 0.02 and 1.00 Pa. The sample grown under vacuum (PO2 = 0.00 Pa) shows mixed Cu oxidation state of 1 + or 2 + . The sample grown without oxygen is n-type and those grown with oxygen are highly insulating. The insulating sample grown at PO2 = 0.02 Pa shows highest magnetization due to possible collective behavior of Cu2+ – O v – Cu2+ network in the form of bound magnetic polaron (BMP) and ferromagnetic superexchange interaction coming from uncompensated surface spins of the Cu ions in the CuO secondary phase. Both delocalized electrons (∼3.32 × 1018) due to oxygen deficient defects and reduced amount of effective Cu2+ ions discredit the BMP model for this vacuum grown sample, and magnetism is suggested due to O v and presence of possible CuO secondary phase.