In this paper we have performed density-functional study on the adsorption and diffusion of various alkali-metal ions on the surface of pristine and defective armchair single-wall carbon nanotubes. In the pristine SWNT system, the position above the hexagon is believed to be the most stable site for adsorption, while the adsorption is enhanced in the defective SWNT. In pristine SWNT all the ions prefer to diffuse along the axial direction, with low barriers less than 0.25 eV. In defective SWNT, the axial diffusion is also energetically most preferable, and the barriers increase only slightly and have little influence on the diffusion as compared to pristine SWNT.