Hydrogen has become a strong candidate to be a future energy storage medium but there are technological challenges both in its production and storage. For storage, a search for lightweight, abundant and non-toxic materials is on the way. An abundant natural material such as wood cellulose would make an ideal storage medium from a sustainability perspective. Here, using a combination of static DFT calculations and ab initio molecular dynamics simulations at different temperatures, it is shown that wood cellulose has the ability to uptake H-2 via a physisorption mechanism based on dispersion interactions of the van der Waals type involving the O-atoms of the D-glucose rings. The absorption causes little to no disturbances on the cellulose structure and H-2 is highly mobile in the material. At an external pressure of H-2(g) of 0.09 atm and T = 25 degrees C, cellulose has a theoretical gravimetric density of hydrogen storage of approximate to 1%.