Hydrogen adsorption in multi-walled boron nitride nanotubes and their arrays was studied using grand canonical Monte Carlo simulation. The results show that hydrogen storage increases with tube diameter and the distance between the tubes in multi-walled boron nitride nanotube arrays. Also, triple-walled boron nitride nanotubes present the lowest level of hydrogen physisorption, double-walled boron nitride nanotubes adsorb hydrogen better when the diameter of the inner tube diameter is sufficiently large, and single-walled boron nitride nanotubes adsorb hydrogen well when the tube diameter is small enough. Boron nitride nanotube arrays adsorb hydrogen, but the percentage of adsorbed hydrogen (by weight) in boron nitride nanotube arrays is rather similar to that found in multi-walled boron nitride nanotubes. Also, when the Langmuir and Langmuir–Freundlich equations were fitted to the simulated data, it was found that multi-layer adsorptivity occurs more prominently as the number of walls and the tube diameter increase. However, in single-walled boron nitride nanotubes with a small diameter, the dominant mechanism is monolayer adsorptivity.