The adsorption of molecular hydrogen on boron nitride nanotubes is studied with the use of the pseudopotential density functional method. The binding energy and distance of adsorbed hydrogen is particularly calculated. It is found that the binding energy of hydrogen on boron nitride nanotubes is increased by as much as 40% compared to that on carbon nanotubes, which is attributed to heteropolar bonding in boron nitride. The effect of substitutional doping and structural defects on hydrogen adsorption is also studied and we find a substantial enhancement of the binding energy from that on perfect boron nitride. The current study demonstrates a pathway to the finding of proper media that can hold hydrogen at ambient conditions through physisorption.