  We calculate the relic density of stau at the beginning of the Big-Bang
Nucleosynthesis (BBN) era in the coannihilation scenario of minimal
supersymmetric standard model (MSSM). In this scenario, stau can be long-lived
and form bound states with nuclei. We put constraints on the parameter space of
MSSM by connecting the calculation of the relic density of stau to the
observation of the light elements abundance, which strongly depends on the
relic density of stau. Consistency between the theoretical prediction and the
observational result, both of the dark matter abundance and the light elements
abundance, requires the mass difference between the lighter stau and the
lightest neutralino to be around 100MeV, the stau mass to be 300 -- 400 GeV,
and the mixing angle of the left and right-handed staus to be
$\sin\theta_{\tau} = (0.65 \textrm{--} 1)$.
