  The discrepancy between the theoretical prediction of primordial lithium
abundances and astronomical observations is called the Lithium Problem. We find
that extra contributions from non-thermal hydrogen and helium during Big Bang
nucleosynthesis can explain the discrepancy, for both Li-7 and Li-6, and will
change the deuterium abundance only little. The allowed parameter space of such
an amount of non-thermal particles and the energy range is shown. The
hypothesis is stable regardless of the cross-section uncertainty of relevant
reactions and the explicit shape of the energy spectrum.
