Using first-principles calculations, we report the adsorption of adenine dinucleoside on single-walled carbon nanotubes (CNTs) with various diameters and chiral angles. The calculations indicate that in addition to noncovalent pi-pi interactions between the adenine base of dinucleoside and CNT, hydrogen bond interactions also develop between the sugar residue and the pi orbital of CNT. The adsorption energy for the dinucleoside is between 1.50 and 3.80 eV for different CNTs. It exhibits a pronounced and specific dependence on the CNT band gap and diameter. For semiconducting zigzag CNTs, the adsorption energy decreases with increasing band gap. For armchair CNTs the adsorption energy increases with increasing diameter.