DFT calculations have been performed to study noncovalent interactions of a hydrogen molecule and single-walled carbon nanotubes (SWCNTs) of various diameters. Understanding these interactions is crucial for the development of systems for hydrogen storage and delivery. The barrier and barrier-free introduction of a hydrogen molecule into SWCNTs is observed. It has been found that hydrogen molecules bind differently onto SWCNTs, depending on their diameters and the orientation of an H2 molecule inside the SWCNT. The binding inside SWCNTs with small diameters ((3,3); (4,4)) is very unfavorable; the opposite situation is in the case of larger ((5,5); (6,6)) SWCNTs. Finally, in the case of ((7,7); (8,8)) SWCNTs, the hydrogen binding energies decrease, and their values approach to those of graphene.