The adsorption of atomic and molecular hydrogen on zigzag and armchair AlN nanotubes is investigated within the ab initio density functional theory. The adsorption configurations are magnetic when the H atom is adsorbed on the Al atom and the center of a hexagon. The total magnetic moment is 1.00 mu B which comes from the H atom and the nearest neighbor N atoms. The barrier height of various adsorption configurations is very low, indicating that the adsorbed H atom can easily transform into other forms. The adsorption energies of hydrogen atoms to the zigzag and armchair AlN nanotubes are calculated at 25%, 50%, 75%, 100%, 133%, and 200% coverages, the most favorable adsorption configurations are 100% hydrogen coverages. The adsorption configuration of hydrogen molecule adsorbed on the Al atom is the most energetically favorable. Each Al atom is capable of binding one hydrogen molecule, corresponding to the hydrogen gravimetric density to 8.89 wt%. Our theoretical study demonstrates that AlN nanotube can be a potential candidate for the hydrogen storage materials. (C) 2015 Elsevier B.V. All rights reserved.