Self-assembling cyclic D,L-peptide nanotubes are electronically insulating and possess wide band gaps (E-g > 4eV). Our ab initio electronic structure calculations indicate that the presence of aromatic rings in the side chain of peptide nanotubes significantly reduces the band gap. We investigate the conductivity of the modified peptide nanotubes through calculations of the electron tunneling probability. The electron tunneling probability through a molecule depends on the length of the molecule, L, as e(-beta(E)L), where the tunneling beta(E)-factor is strongly energy-dependent. We have calculated beta(E) in three types of peptide nanotubes that have different sequences of amino acid residue, (L-Gln, D-Ala)(4), (L-Gln, D-Leu)(4) and (L-Gln, D-Phe)(4), using the complex band structure approach. We find large beta values near midgap, making these peptide nanotubes a poor tunneling conductor.