In this article, the grand canonical Monte Carlo (GCMC) method included in GULP software system is adopted to study the hydrogen storage properties of armchair-type single-walled carbon nanotubes (SWNT) with at the low and normal temperatures. The adsorption isotherms with five different radii of SWNT at T=77 K and T=280 K are obtained. The manifold configuration diagrams of hydrogen molecule in the carbon nanotubes with the same caliber at different temperatures and pressures are also given. A further study on hydrogen physisorption is carried out under different pressures and different diameters of carbon nanotubes, separately, at temperatures of 77 K and 280 K, and the results are compared with each other. Finally, we put forward some constructive suggestions about how to improve the adsorption capacity of SWNT according to the results of our GCMC simulation. This may be useful for further investigation.