The adsorption of molecular hydrogen gas onto charged single-walled carbon nanotubes (SWNTs) is studied by grand canonical Monte Carlo (GCMC) computer simulation. The quadrupole moment and induced dipole interaction of hydrogen with "realistically" charged (0.1 e/C) nanotubes leads to an increase in adsorption relative to the uncharged tubes of similar to 10%-20% for T = 298 K and 15%-30% for 77 K. Long-range electrostatic interactions makes second layer (exohedral) adsorption significantly higher. Hydrogen orientation-ordering effects and adsorption anisotropy in the electrostatic field of the nanotube were observed. The geometry of nanotube arrays was optimized at fixed values of charge, temperature, and pressure. In general, negatively charged nanotubes lead to more adsorption because the quadrupole moment of hydrogen is positive. Calculated isotherms indicate that even charged nanotube arrays are not suitable sorbents for achieving the DOE target for hydrogen transportation and storage at normal temperatures, unless the charges on the nanotubes are unrealistically large.