The adsorptions of hydrogen both on square-packed single-walled carbon nanotube (SWCNT) arrays and on isolated nanotubes were investigated by a combination of a classical potential and density functional theory (DFT) method. Excess adsorption of hydrogen on the SWCNT with diameters of 1.225, 2.04, and 2.719 nm at 77 K and at ambient temperature, T = 300 K, has been calculated. DFT calculations indicate that the excess gravimetric storage capacity of exohedral adsorption of hydrogen on SWCNT array is as much as 30% of that of endohedral adsorption when the van der Walls (VDW) gap was fixed at 0.335 run, while excess adsorption of hydrogen outside the nanotubes is close to or exceeds the excess endohedral adsorption for isolated nanotubes. The total excess gravimetric storage capacity (including endohedral and exohedral adsorptions) of hydrogen on open nanotube arrays of 2.719 nm is 7.1 wt % at 77 K and 4 MPa, while the total excess adsorption of hydrogen on open isolated nanotubes of 2.719 nm reaches 9.5 wt % at the same temperature and pressure. The two results both reach the gravimetric density of Department of Energy (DOE) target, 6.5 wt %, which means that the adsorption storage of hydrogen on SWCNTs has a practical significance. However, the total excess adsorption of hydrogen both on carbon nanotube arrays and on isolated nanotubes at 300 K does not exceed I wt % in the range of pressures that we studied and almost linearly increases with the increase of pressure. This is because the hydrogen molecules have enough kinetic energy to overcome the adsorption potential of SWCNTs at T = 300 K. For carbon nanotube arrays, the effect of VDW gap on hydrogen adsorption was investigated. Results indicate that in the range from 0.335 to 2.0 nm a larger VDW gap implies a greater excess gravimetric capacity and a smaller volumetric storage capacity, simultaneously. In addition, we also note that the choice of method used to determine the bulk density is key because it significantly affects the excess adsorption of hydrogen. In this work, DFT method is used to determine both the gas density in the confined space and the density in the bulk states simultaneously. It is more accurate than MBWR equation of state in solving the bulk density. In short, the predicted results of hydrogen storage capacities in SWCNTs at T = 300 and 77 K in this work are in reasonable agreement with experimentally measured data.