Global warming due to excessive use of fossil fuels has driven researchers to focus on sustainable energy sources for the future. For clean production systems, biofuel is expanding the domain of renewable and sustainable energy supplies. An efficient and sustainable supply chain plays a pivotal role in ensuring this supply. In this research, crop residuals in different agricultural zones, transportation for shipment of residual biomass as well as biofuel, multiple biorefineries, and multiple market centers are considered. The expense of the resources, the yield of residual biomass in agricultural zones, and the demand of market centers are represented by fuzzy numbers as they are assumed to be uncertain. The carbon emissions cost at all stages of the supply chain was also incorporated into this model. This objective of this study is to develop a supply chain model that minimizes the total cost of a second generation biofuel supply chain and location-allocation for agricultural zones and biorefineries to meet the uncertain demand for market centers. Two numerical examples are analyzed, and the results proves that the cost of biofuel production in biorefineries contributed 52.16%, which is a major proportion of the total cost. In the entire supply chain, the transportation sector is the foremost source of carbon emissions in an environment with 88.50% of the total carbon emissions. The results confirms that the proposed model is viable for designing second generation biofuel supply chains under uncertainty. Significant managerial insights of this research are also described to better express the efficiency of the model.