The effect of high-pressure torsion (HPT) on the microstructure and hardness of Cu–carbon nanotube (CNT) nanocomposite and unreinforced Cu, processed by mechanical ball-milling and hot pressing, were investigated. High-resolution transmission electron microscopy observation revealed arrays of equiaxial grains with average grain sizes of 128 nm and 140 nm for the nanocomposite and Cu, respectively, and strong interfaces between Cu and CNTs after HPT. The addition of CNTs to Cu resulted in further increase in microstrain and decrease in the mean grain size of the nanocomposite. Our findings indicate misorientation between Cu and CNTs at their interface, (i.e., a gradual transition from the lattice planes of face-centered cubic Cu to those of the CNT). Hardness evaluation of the Cu–4 vol% CNT nanocomposite indicates high microhardness (2.01 GPa), 16.8% higher than that of the nanostructured Cu. The high microhardness of the nanocomposite is due to the nanostructured Cu matrix, uniform distribution of the CNTs, and modified Cu–CNT interface that resulted from the combined processing. Strengthening mechanisms, relative to the microstructural features of the nanocomposite, are discussed.