We review a non-standard Big-Bang Nucleosynthesis (BBN) scenario within the minimal supersymmetric standard model, and propose an idea to solve both 7 Li and 6 Li problems. Each problem is a discrepancy between the predicted abundance in the standard BBN and observed one. We focus on the stau, a supersymmetric partner of tau lepton, which is a long-lived charged particle when it is the next lightest supersymmetric particle and is degenerate in mass with the lightest supersymmetric particle. The long-lived stau forms a bound state with a nucleus, and provide non-standard nuclear reactions. One of those, the internal conversion process, accelerates the destruction of 7 Be and 7 Li, and leads to a solution to the 7 Li problem. On the other hand, the bound state of the stau and 4 He enhances productions of n, D, T, and 6 Li. The over-production of 6 Li could solve the 6 Li problem. While, the over-productions of D and T could conflict with observations, and the relevant parameter space of the stau is strictly constrained. We therefore need to carefully investigate the stau-4 He bound state to find a condition of solving the 6 Li problem. The scenario of the long-lived stau simultaneously and successfully fit the abundances of light elements (D, T, 3 He, 4 He, 6 Li, and 7 Li) and the neutralino dark matter to the observed ones. Consequently parameter space both of the stau and the neutralino is determined with excellent accuracy. *