Nanodispersion of single-walled carbon nanotubes (SWCNTs) has been systematically investigated with the use of sodium dodecyl sulfate (SDS) and poly(vinylpyrrolidone) (PVP) surfactant in de-ionized water. A high concentration of nanodispersed SWCNTs up to 0.08 mg/mL was achieved with introduction of an additional dispersant of PVP by optimizing surfactant concentration, sonication time, and centrifugation speed, which was crucial to obtaining a high concentration of SWCNTs in the supernatant solution. We also demonstrate that diameters of the nanodispersed nanotubes can be sorted out by controlling the centrifugation speed and furthermore the saturated SWCNT concentration was nearly constant, independent of the initial concentration at high centrifugation speed. Two dispersion states were identified depending on the centrifugation speed: an intermediate dispersion of nanodispersion mixed with macrodispersion (I) and nanodispersion (II). This was verified by Raman spectroscopy, scanning probe microscopy, optical absorption spectroscopy, and photoluminescence measurements. The obtained SWCNT solution was stable up to about ten days. Some aggregated SWCNT solution after a long period of time was fully recovered to initial state of dispersion after re-sonication for a few minutes. Our systematic study on high concentration nanodispersion of SWCNTs with selective diameters provides an opportunity to extend the application areas of high quality SWCNTs in large quantity.