The aim of this study is the preparation of nanostructured copper(II) oxide-based materials (CuONPs) through a facile additive-free polyol procedure that consists of the hydrolysis of copper(II) acetate in 1,4-butane diol and its application in hydrogen peroxide sensing. The nonenzymatic electrochemical sensor for hydrogen peroxide determination was constructed by drop casting the CuONP sensing material on top of a glassy carbon electrode (GCE) modified by a layer of poly(3,4-ethylenedioxythiophene) conducting polymer (PEDOT). The PEDOT layer was prepared on GCE using the sinusoidal voltage method. The XRD pattern of the CuONPs reveals the formation of the monoclinic tenorite phase, CuO, with average crystallite sizes of 8.7 nm, while the estimated band gap from UV–vis spectroscopy is of 1.2 eV. The SEM, STEM, and BET analyses show the formation of quasi-prismatic microaggregates of nanoparticles, with dimensions ranging from 1 µm up to ca. 200 µm, with a mesoporous structure. The developed electrochemical sensor exhibited a linear response toward H2O2 in the concentration range from 0.04 to 10 mM, with a low detection limit of 8.5 μM of H2O2. Furthermore, the obtained sensor possessed an excellent anti-interference capability in H2O2 determination in the presence of interfering compounds such as KNO3 and KNO2.