The hybrids of single-walled carbon nanotube.(SWCNT) and single,stranded DNA (ssDNA) are novel nanoscale materials having, remarkable:,applications in nanotechnology. The absorption of nucleobases on the surface of a SWCNT depends strongly on: the ionic strength of the medium. In this paper, using atomistic molecular dynamics we have shown that at low salt concentration ssDNA wraps on the surface of SWCNT through hydrophobic pi-pi stacking between the DNA-bases and the sp(2)-hybridized carbon atoms of the carbon nanotube. At high salt concentration, however; the DNA-Molecule adopts a partially folded structure and the ssDNA-SWCNT wrapping gets weakened significantly due to the self-stacking of the DNA bases. Our study can find relevance in CNT mediated gene delivery processes where subsequent unwrapping of the gene from its carrier is anticipated across the cell membrane regulated by an existing salt concentration gradient.