Cu2O is a direct and narrow band-gap material; hence, it serves as an important candidate material for applications such as solar cells. In this study, copper (Cu) metal was used as a target and the reactive sputtering method was used to deposit cuprous oxide (Cu2O) and cupric oxide (CuO) thin films on indium tin oxide (ITO) glass. The formation of Cu2O and CuO thin films was controlled by varying oxidation conditions, such as controlling the deposition atmosphere (called the O2 ratio). The microstructure, crystalline orientation, and optical properties of Cu2O and CuO thin films were measured using X-ray diffraction and optical spectroscopy, respectively. The results for the deposited thin films indicated that the formation of thin films as Cu2O and CuO phases was controlled by the flow rate of oxygen during the deposition process. In addition, the (αhv)n–hν curve plot was used to find the optical energy band gap of the Cu2O and CuO thin films. Moreover, we found that the crystalline phase and morphology of the deposited thin films affected the properties of the spectral response. This study provides a reference for the possible exploration and application of new, high-performance thin-film photovoltaic solar cells.