Background: Population growth and increasing the utilization of fossil fuels have increased carbon emissions and the global warming phenomenon with detrimental impacts on the human life and the environment. Therefore, finding a sustainable substitution for fossil fuels becomes a great challenge for all societies from all over the world. Renewable energies such as biofuels are the appropriate alternative to decrease environmental concerns.Methods: This study develops a multi-objective multi-period multi-echelon biofuel supply chain (BSC) from switch grass regarding economic, environmental and social aspects of the sustainability. For considering the environmental aspect, four carbon policies are taken into account; namely the carbon cap, the carbon tax, the carbon trade and the carbon offset. The fuzzy interactive programming method is implemented to solve the multi-objective model and the fuzzy best-worst method (FMWM) is applied for weighting social objective components.Results: To illustrate the applicability of the model, an actual case study in Iran is considered. It is revealed that different solutions are obtained for the location of switch grass resources, preprocessing centers, and bio-refineries under different carbon policies. Numerical results also demonstrate that biofuel production and transportation activities have a great share in carbon emissions and BSC costs. Applying the carbon cap policy in the proposed case study decreases the carbon emission over 14% in comparison to the basic situation. Moreover, implementing the carbon trade policy increases the total BSC profit about 11% in comparison to the basic situation. The carbon offset policy plays a significant role in improving social considerations compared with other policies. Overall, since three aspects of sustainability have appropriate values under the carbon trade policy, it can be concluded that this policy is the most appropriate policy.Conclusions: The proposed model can aid policy makers and governments to optimize the profitability of the BSC, the carbon emission reduction, and the social consideration, simultaneously.