The hydrogen adsorption on La-doped single BN nanotubes were investigated by first-principles based on density functional theory. Our calculated results show that the binding energy of La metal is large enough and ensure the stability toward recyclability. The maximum of six hydrogen molecules be adsorbed on the La-doped BN nanotube which can store up to 4.50 wt%. The density of states show that hybridizations between La-5p,5d ,6s states and B-2p, C-2p orbitals appear near the Fermi level. It is clear that the positive charge of La cation can polarize the incoming H2 molecules. The research of this paper has a certain guiding significance for the synthesis of high performance BN nanotube hydrogen storage materials.