Atomistic models of quasi-one-dimensional vanadium pentoxide nanostructures - single-walled nanotubes formed by rolling (010) layers of V2O5 are constructed and their electronic properties and bond indices are studied using the tight-binding band method. We show that all zigzag (n,0)- and armchair (n,n)-like nanotubes are uniformly semiconducting, and the band gap trends to vanish as the tube diameters decrease. The V-O covalent bonds were found to be the strongest interactions in V2O5 tubes, whereas V-V bonds proved to be much weaker.