The influences of annealing temperature on the wear properties and electrical conductivity of Cu were studied after processing by high-pressure torsion (HPT). The annealing of Cu specimens processed by HPT leads to an increase in electroconductivity and a decrease in the wear rate. It is apparent that a nanotribolayer at the surface induced during wear sliding plays a more significant role than the ultrafine-grained structure. A slight increase was observed in the microhardness of HPT copper specimens upon annealing at a relatively low temperature (100 °C), and this is most likely due to a change in texture. The annealing leads to an increase in the Taylor factor by ∼5 %, which is in good agreement with the increase in the microhardness level which is also by ∼5 %. It is apparent that low-temperature annealing of HPT copper may produce optimal properties of the specimens including high strength and electroconductivity with a lower wear rate.