Using ab initio calculations we investigated the hydrogen storage in single-walled carbon nanotubes (SWNT). We present the calculated nuclear quadrupole coupling constants (NQCCs) of absorbed hydrogen atom both in interior and exterior situation of some zigzag and armchair carbon nanotubes (CNTs). In addition, the effect of substitution of heteroatoms such as boron and nitrogen in CNTs network on calculated NQCC of absorbed hydrogen atom was investigated. In continue, some metal atom and their ion encapsulating inside (5, 0) CNT were considered and 2 H-NQCCs of absorbed hydrogen atom were calculated. In the presence of Cu +2 in (5, 0) CNT, charge transfer from hydrogen to CNT is more complete and the absorbed hydrogen atom has better interaction with carbon. The electric field gradient (EFG) at the site of quadrupolar nuclei were calculated to obtain NQCC parameters using Gaussian 98 at HF/3-21G level of theory. The selected level and basis set give the rather acceptable qualitative NQCCs of hydrogen atoms.