Carbon nanotubes (CNTs) and helical nanofibers (HNFs) were selectively grown on copper substrates by chemical vapor deposition using acetylene as a carbon source. The experiments were carried out by using Ni, Fe and Co as single and co-catalysts which were deposited onto the substrates by a sparking method. The catalyst-coated copper substrates were heated at 750°C in a mixed-gas-flowing tube furnace, at an argon flow rate of 100 ml/min and various acetylene flow rates of 3, 5 and 10 ml/min. The larger diameter of HNFs was grown only on Ni and Ni-Fe catalysts at the acetylene flow rates of 5 and 10 ml/min whereas the uniform smaller diameter of CNTs was preferentially grown on Fe-Co and Ni-Fe catalysts at the flow rate of 3 ml/min. We suggest that Co likely prevents the formation of HNFs whereas Ni promotes.