Using density functional theory we show that an applied electric field substantially improves the hydrogen storage properties of a BN sheet by polarizing the hydrogen molecules as well as the substrate. The adsorption energy of a single H2 molecule in the presence of an electric field of 0.05 a.u. is 0.48 eV compared to 0.07 eV in its absence. When one layer of H2 molecules is adsorbed, the binding energy per H2 molecule increases from 0.03 eV in the field-free case to 0.14 eV/H2 in the presence of an electric field of 0.045 a.u. The corresponding gravimetric density of 7.5 wt % is consistent with the 6 wt % system target set by DOE for 2010. Once the applied electric field is removed, the stored H2 molecules can be easily released, thus making the storage reversible.