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Adsorption of hydrogen molecules on platinum-doped single-walled zigzag (8,0) boron nitride (BN) nanotube is investigated using the density-functional theory. The Pt atom tends to occupy the axial bridge site of the BN tube with the highest binding energy of −0.91 eV. Upon Pt doping, several occupied and unoccupied impurity states are induced, which reduces the band gap of the pristine BN nanotube. Upon hydrogen adsorption on Pt-doped BN nanotube, the first hydrogen molecule can be chemically adsorbed on the Pt-doped BN nanotube without crossing any energy barrier, whereas the second hydrogen molecule has to overcome a small energy barrier of 0.019 eV. At least up to two hydrogen molecules can be chemically adsorbed on a single Pt atom supported by the BN nanotube, with the average adsorption energy of −0.365 eV. Upon hydrogen adsorption on a Pt-dimer-doped BN nanotube, the formation of the Pt dimer not only weakens the interaction between the Pt cluster and the BN nanotube but also reduces the average adsorption energy of hydrogen molecules. These calculation results can be useful in the assessment of metal-doped BN nanotubes as potential hydrogen storage media.