Density functional theory (DFT) has been employed to investigate hydrogen physisorption on very narrow (diameter: d < 6 angstrom) single wall carbon nanotubes (SWCNTs). Equilibrium deposition sites and binding energy for a single hydrogen molecule have been studied through exo- and endo-hydrogenations. Effects of chirality, diameter and also the orientation of the molecule against the SWCNTs, have been under consideration, as well. The narrow SWCNTs with different chiralities and roughly same radius have very different binding energies for the H-2 adsorption in endo-hydrogenation. Incidentally, the calculations show that the binding energy for hydrogen molecule inside the nanotubes is approximately two times higher than the outside adsorption. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.