  A scenario of the Big-Bang Nucleosynthesis is analyzed within the Minimal
Supersymmetric Standard Model which is consistent with a stau-neutralino
coannihilation scenario to explain the relic abundance of dark matter. We find
that we can account for the possible descrepancy of the abundance of
$\mathrm{^{7}Li}$ between the observation and the prediction of the Big-Bang
Nucleosynthesis by taking the mass of the neutralino as $300 \mathrm{GeV}$ and
the mass difference between the stau and the neutralino as $(100 -- 120) MeV$.
We can therefore simultaneously explain the abundance of the dark matter and
that of $\mathrm{^{7}Li}$ by these values of parameters. The lifetime of staus
in this scenario is predicted to be $O(100 -- 1000) sec$.
