Using first-principles calculations, the adsorption and storage of hydrogen molecules on Y decorated B38 fullerene (Y4@B38) are investigated. It is shown that Y atoms strongly attach to the hexagon cavities of B38, and that isolated Y atoms on B38 are energetically more stable than the Y4 cluster, hence avoiding the aggregation issue. Moreover, Y4@B38 weakly interact with each other to build larger clusters. Polarization effects, as well as the Kubas mechanism, play essential roles in H2 adsorption and storage on Y4@B38. The adsorption energy per H2 molecule on Y4@B38 ranges from -0.180 to -0.249 eV, which is within the recommended range for an optimal H2 storage material. Each Y atom in Y4@B38 may hold up to six H2 molecules, corresponding to a gravimetric density of 4.96 %. The stability of H2 adsorbed structures and its dependence on temperature and pressure are evaluated using the modified van’t Hoff equation.