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We calculate the relic density of stau at the beginning of the Big-BangNucleosynthesis (BBN) era in the coannihilation scenario of minimalsupersymmetric standard model (MSSM). In this scenario, stau can be long-livedand form bound states with nuclei. We put constraints on the parameter space ofMSSM by connecting the calculation of the relic density of stau to theobservation of the light elements abundance, which strongly depends on therelic density of stau. Consistency between the theoretical prediction and theobservational result, both of the dark matter abundance and the light elementsabundance, requires the mass difference between the lighter stau and thelightest 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$\sin\theta_{\tau} = (0.65 \textrm{--} 1)$.

Stau relic density at the Big-Bang nucleosynthesis era consistent with the abundance of the light element nuclei in the coannihilation scenario