Enhanced manipulation and analysis of bio-particles using light confined in nano-scale dielectric structures has proceeded apace in the last several years. Small mode volumes, along with the lack of a need for bulky optical elements give advantages in sensitivity and scalability relative to conventional optical manipulation. However, manipulation of lipid vesicles (liposomes) remains difficult, particularly in the sub-micron diameter regime. Here we demonstrate the optical trapping and transport of sub-micron diameter liposomes along an optical nanofiber using the nanofiber mode's evanescent field. We find that nanofiber diameters below a nominal diffraction limit give optimal results. Our results pave the way for integrated optical transport and analysis of liposome-like bio-particles, as well as their coupling to nano-optical resonators.