Hydrogen storage in single walled carbon nanotubes (SWNTs) is studied by grand canonical Monte Carlo (GCMC) simulation. Hydrogen-hydrogen and hydrogen-carbon interactions are both modeled with Lennard-Jones potential. Hydrogen-carbon interactions are integrated over the whole nanotube to get molecule-tube interactions. Three adsorption isotherms of different diameters at 293.15 K, one adsorption isostatics at 2.66 MPa with radius of 0.587 nm, the amount of adsorption as a function of van der Waals (VDW) distance of nanotubes with the three diameters at 3 MPa (where the VDW distance is defined as the distance between the walls of the nearest neighbor tubes in the bundle, as measured from the carbon centers) and the adsorption as function of continuously changing diameter are displayed. Finally, the influences of pressures, temperatures, the diameters and VDW distances of SWNTs on adsorption are discussed.