The structural, energetic and electronic properties of chiral (n, m) (3⩽n⩽6, n/2⩽m⩽n) single-wall copper nanotubes (CuNTs) have been investigated by using projector-augmented wave method based on density-functional theory. The (4, 3) CuNT is energetically stable and should be observed experimentally in both free-standing and tip-suspended conditions, whereas the (5, 5) and (6, 4) CuNTs should be observed in free-standing and tip-suspended conditions, respectively. The number of conductance channels in the CuNTs does not always correspond to the number of atomic strands comprising the nanotube. Charge density contours show that there is an enhanced interatomic interaction in CuNTs compared with Cu bulk. Current transporting states display different periods and chirality, the combined effects of which lead to weaker chiral currents on CuNTs.