The surface wettability of a liquid on the inner and outer surface of single carbon nanotubes (CNTs) was experimentally investigated. Although these contact angles on both surfaces were previously studied separately, the available data are of limited help to elucidate the effect of curvature orientation (concave or convex) on wettability due to the difference in surface structure. Here, we report on the three-phase contact region and wettability on the outer surface of CNT during the dipping and withdrawing experiment of CNT into an ionic liquid. Furthermore, the wettability on the inner surface was measured using a liquid within the same CNT. Our results show that the contact angle on the outer surface of the CNT is larger than that on the flat surface and that on the inner surface is smaller than that on the flat one. These findings suggest that the surface curvature orientation has a noticeable effect on the contact angle at the nanoscale because both inner and outer surfaces expose the same graphite wall structure and the contact line tension will be negligible in this situation. The presented results are rationalized using the free energy balance of liquid on curved surfaces.