We report molecular dynamics simulations of DNA adsorption on a single-walled carbon nanotube (SWNT) in an aqueous environment. We have modeled a DNA segment with 12 base pairs (Dickerson dodecamer) and a (8,8) SWNT in water, with counterions to maintain total charge neutrality. Simulations show that DNA binds to the external surface of an uncharged or positively charged SWNT on a time scale of a few hundred picoseconds. The hydrophobic end groups of DNA are attracted to the hydrophobic SWNT surface of uncharged SWNTs, while the hydrophilic backbone of DNA does not bind to the uncharged SWNT. The binding mode of DNA to charged SWNTs is qualitatively different from uncharged SWNTs. The phosphodiester groups of the DNA backbone are attracted to a positively charged SWNT surface while DNA does not adsorb on negatively charged SWNTs. There is no evidence for canonical double-stranded DNA wrapping around either charged or uncharged SWNTs on the very short time scales of the simulations. The adsorption process appears to have negligible effect on the internal stacking structure of the DNA molecule but significantly affects the A to B form conversion of A-DNA. The adsorption of A-DNA onto an uncharged SWNT inhibits the complete relaxation of A-DNA to B-DNA within the time scale of the simulations. In contrast, binding of the A-DNA onto a positively charged SWNT may promote slightly the A to B conversion.