Grand Canonical Monte Carlo(GCMC) method was employed to simulate the adsorption properties of molecular hydrogen on NaA zeolite at 40-293 K and pressures up to 10000 kPa in this paper. The results indicated that the adsorption capacity of hydrogen increased with decreasing temperatures and increasing pressures. The highest hydrogen uptake value is 1.54 wt.% at 40 K and 10000kPa. Adsorption temperature has an important effect on adsorption energies and adsorption sites of hydrogen molecules in NaA zeolite. For lower temperature (below 180 K), the oxygen atoms of zeolite framework and extra-framework cations are stable adsorption sites of hydrogen molecules. For the higher temperatures (above 180 K), the oxygen atoms are only stable adsorption sites of hydrogen molecules.