We report a first-principles investigation of Li adsorption and diffusion in single-walled Si nanotubes (SWSiNTs) of interest to Li-ion battery anodes. We calculate Li insertion characteristics in SWSiNTs and compare them with the respective ones in carbon nanotubes (CNTs) and other silicon nanostructures. From our calculations, SWSiNTs show higher reactivity toward the adsorption of Li adatoms than CNTs and Si nanoclusters. Considering the importance of Li kinetics, we demonstrate that the interior of SWSiNTs may serve as a fast Li diffusion channel. The important advantage of SWSiNTs over their carbon analogues is a sevenfold reduction in the energy barrier for the penetration of the Li atoms into the nanotube interior through the sidewalls. This prepossesses easier Li diffusion inside the tube and subsequent utilization of the interior sites, which enhances Li storage capacity of the system. The improvements in both Li uptake and Li mobility over their analogues support the great potential of SWSiNTs as Li-ion battery anodes.