One of the primary challenges to introduce hydrogen on the energy market is to improve onboard hydrogen storage and research more efficient distribution technologies to increase the amount of stored gas while lessening the storage pressure. The aim of this paper is to study hydrogen storage in an on-board hydrogen adsorption storage tank under low temperature and moderate pressures through the finite element analysis software Comsol MultiphysicsTM. The experimental study is carried out in a cylindrical tank with granular adsorbents in which the bed temperature is measured at various positions. The adsorbents we used in the experiment are activated carbon (NORIT R0.8) and metal-organic framework (Cu-BTC). Compared with the experiment results, the simulated pressure and temperature of the activated carbon (NORIT R0.8) have better agreement with experimental results than the metal-organic framework (Cu-BTC). The material properties of Cu-BTC are necessary to be identified accurately. Owing to the mass flow rate controlled comparatively accurate, the simulated mass balance have a good accordance with the experiment results. The effective thermal conductivity of the adsorbent bed and the heat transfer coefficient of the tank wall with liquid nitrogen affect significantly the heat transport during the adsorption process. The simulation results are very sensitive with the boundary type of inlet and other outer boundaries of the tank, which is valuable for further study.