The first-principles plane-wave pseudopotential method within density functional theory formalism is used to investigate the effect of Y atom decoration of graphene on the properties for hydrogen storage. The clustering problem for the Y atoms decorated on graphene is considered, and substitutional boron doping is shown to effectively prevent the clustering of Y atoms on graphene. The geometrical configuration of the modified system is stable and the adsorption properties of H2 are excellent, which can adsorb up to 6 H2 molecules with an average adsorption energy range of-0.539 to-0.655 eV (per H2), as determined by theoretical analyses. This satisfies the theoretical ideal range for hydrogen storage. Moreover, based on the calculation and analysis of the Bader charge, the electronic density of states and the charge density difference of the H2/Y/B/graphene (G) system, it is proved that the Y atom exhibits bonding with graphene by charge transfer and interacts with hydrogen molecules through typical Kubas interactions. The existence of the Y atom alters the charge distribution of the H2 molecules and graphene sheet. Hence, the Y atom becomes a bridge linking the H2 molecules and graphene sheet. Thereby, the adsorption energies of the H2 molecule are adjusted to the reasonable region. The modified system exhibits excellent potential as one of the most suitable candidates for a hydrogen storage medium in the molecular state at near ambient conditions.