We investigate the interaction of a hydrogen atom with an armchair-type, single-walled carbon nanotube, based on the density functional theory (DFT), and discuss how changes in the nanotube's diameter affect hydrogen adsorption on the carbon nanotube. We find that because the strong sp2-like bonding and π-bonding network are enhanced with increasing nanotube diameter, hydrogen adsorption on the carbon nanotube becomes less stable with increasing nanotube diameter. We also find that with increasing nanotube diameter, the potential energy curves approach that for hydrogen interacting with a graphene sheet. These results can be explained in terms of the hydrogen-induced changes in the local density of states of the carbon nanotube.