  There may be non-thermal cosmic rays during big-bang nucleosynthesis (BBN)
epoch (dubbed as BBNCRs). This paper investigated whether such BBNCRs can be
the origin of Lithium problem or not. It can be expected that BBNCRs flux will
be small in order to keep the success of standard BBN (SBBN). With favorable
assumptions on the BBNCR spectrum between 0.09 -- 4 MeV, our numerical
calculation showed that extra contributions from BBNCRs can account for the
$^7$Li abundance successfully. However $^6$Li abundance is only lifted an order
of magnitude, which is still much lower than the observed value. As the
deuteron abundance is very sensitive to the spectrum choice of BBNCRs, the
allowed parameter space for the spectrum is strictly constrained. We should
emphasize that the acceleration mechanism for BBNCRs in the early universe is
still an open question. For example, strong turbulent magnetic field is
probably the solution to the problem. Whether such a mechanism can provide the
required spectrum deserves further studies.
