First-principles calculations of the atomic and electronic structure of double-wall nanotubes (DWNTs) of a-V2O5 are performed. Relaxation of the DWNT structure leads to the formation of two types of local regions: 1) bulk-type regions and 2) puckering regions. Calculated total density of states (DOS) of DWNTs considerably differ from that of single-wall nanotubes and the single layer, as well as from the DOS of the bulk and double layer. Small shoulders that appear on edges of valence and conduction bands result in a considerable decrease in the band gaps of the DWNTs (up to 1 eV relative to the single-layer gaps). The main reason for this effect is the shift of the inner- and outer-wall DOS in opposite directions on the energetic scale. The electron density corresponding to shoulders at the conduction-band edges is localized on vanadium atoms of the bulk-type regions, whereas the electron density corresponding to shoulders at the valence-band edges belongs to oxygen atoms of both regions.