A multiscale theoretical approach was used for the investigation of hydrogen storage in the recently synthesized carbon nanoscrolls. First, ab initio calculations at the density functional level of theory (DFT) were performed in order to (a) calculate the binding energy of H2 molecules at the walls of nanoscrolls and (b) fit the parameters of the interatomic potential used in Monte Carlo simulations. Second, classical Monte Carlo simulations were performed for estimating the H2 storage capacity of "experimental size" nanoscrolls containing thousands of atoms. Our results show that pure carbon nanoscrolls cannot accumulate hydrogen because the interlayer distance is too small. However, an opening of the spiral structure to approximately 7 A followed by alkali doping can make them very promising materials for hydrogen storage application, reaching 3 wt % at ambient temperature and pressure.