Single-walled carbon nanotubes (SWNTs) are possible nano-injectors and delivery vehicles of molecular probes and drugs into cells. In order to explore the interaction between lipid membranes and carbon nanotubes, we investigate the binding mechanism of dipalmitoylphosphatidylcholine (DPPC) with SWNTs by molecular dynamics. In low concentration range simulations, the DPPC molecules form a supramolecular two-layered cylindrical structure wrapped around the carbon nanotube surface. The hydrophobic part of DPPC is adsorbed on the surface of the nanotube, and the hydrophilic top is oriented towards the aqueous phase. For higher concentration ranges, the DPPC molecules are found to form a supramolecular multi-layered structure wrapped around the carbon nanotube surface. At the saturation point a membrane-like structure is self-assembled with a width of 41.4 angstrom, which is slightly larger than the width of a cell membrane. Our study sheds light on the existing conflicting simulation data on adsorption of single-chained phospholipids.