We study the catalytic capability of unsupported single-walled helical gold nanotubes Au(5,3) by using density functional theory. We use the CO oxidation as a benchmark probe to gain insights into high catalytic activity of the gold nanotubes. The CO oxidation, catalyzed by the Au(5,3) nanotube, proceeds via a two-step mechanism, CO + O2 --> CO2 +O and CO + O --> CO2. The CO oxidation is initiated by the CO + O2 --> OOCO --> CO2 + O reaction with an activation barrier of 0.29 eV. On the reaction path, a peroxo-type O-O-CO intermediate forms. Thereafter, the CO + O --> CO2 reaction proceeds along the reaction pathway with a very low barrier (0.03 eV). Note that the second reaction cannot be the starting point for the CO oxidation due to the energetically disfavored adsorption of free O2 on the gold nanotube. The high catalytic activity of the Au(5,3) nanotube can be attributed to the electronic resonance between electronic states of adsorbed intermediate species and Au atoms at the reaction site, particularly among the d states of Au atom and the antibonding 2pi* states of C-O and O1-O2, concomitant with a partial charge transfer. The presence of undercoordinated Au sites and the strain inherent in the helical gold nanotube also play important roles. Our study suggests that the CO oxidation catalyzed by the helical gold nanotubes is likely to occur at the room temperature.