Cupric oxide (CuO) nanostructure arrays have been extensively investigated for solar energy harvesting, electrochemical energy storage, chemical sensing, field-effect transistors, etc. Although most of these applications depend on the collective behavior of an array of such structures, analysis of electrical transport in a single nanostructure, which are the building blocks, is essential for understanding both the fundamental aspects and device performance. Here we report the electrical conduction mechanism in thermally grown single CuO nanowire (NW), which reveals that the current density has an anomalous dependence on the diameter of the NWs - decreasing with an increase in diameter. An analysis of the electrical behavior at room temperature shows that the current density in CuO NWs has different slopes in different regions of the applied bias indicating distinct types of charge transport, which are characterized as near Ohmic (lower voltage), trap controlled, and space charge limited conduction (higher applied voltage). Further, the trap density and activation energy are calculated from the temperature-dependent current density data, which shows higher values (9.38 × 1015cm-3, 79.4 meV) in thicker NWs compared to that in the thinner ones (3.96 × 1015 cm-3, 63.9 meV). Investigation of the NWs with Raman and photoluminescence spectra establishes the presence of Cu2O phase in thicker NWs, which act as hole traps to hinder the charge transport in p-type CuO and resulting in lower conductivity at higher diameters. This study helps to design and fabricate prototype nanodevices with desired conductivity based on CuO NWs. © 2021 IOP Publishing Ltd.