Today, renewable energy generation infrastructures are increasingly developed due to reduced fossil fuel resources and increased energy consumption. In this respect, a biogas supply chain has a high potential to generate energy. This paper aims to design a bi-objective biogas supply chain network for power and fertilizer generation. A mixed-integer linear programming (MILP) model was developed for the multi-level biogas supply chain with biomass input under different parameter uncertainties. A stochastic-robust programming approach was adopted to cope with the intrinsic uncertainties of such value chains. Realistic uncertainty modeling allowed for adjusting the conservatism level for a trade-off between performance and robustness. The adopted stochastic-robust programming pathway not only diminished the optimality fluctuations and provided a reasonable allocation space for uncertainties but also enhanced network flexibility and alleviated decision-making risks. Finally, the model was solved using the Benders decomposition (BD) algorithm. This research obtained more efficient and effective solutions by enhancing the Benders cuts based on previously generated solutions and Pareto optimal cuts. The implemented algorithm converged to the optimal solution at a reasonable rate.