A comprehensive study was performed on hydrogen adsorption and storage in Ca-coated boron fullerenes and nanotubes by means of density functional computations. Ca strongly binds to boron fullerene and nanotube surfaces due to charge transfer between Ca and the B substrate. Accordingly, Ca atoms do not cluster on the surface of the boron substrate, while transition metals (such as Ti and Sc) persist in clustering on the B(80) surface. B(80) fullerene coated with 12 Ca atoms can store up to 60 H(2) molecules with a binding energy of 0.12-0.40 eV/H(2), corresponding to a gravimetric density of 8.2 wt %, while the hydrogen storage capacity in a (9,0) B nanotube is 7.6 wt % with a binding energy of 0.10-0.30 eV/H(2). The Ca-coated boron fullerenes and nanotubes proposed in this work are favorable for reversible adsorption and desorption of hydrogen at ambient conditions.