Carbon policies refer to governmental and organizational regulations, frameworks, and strategies designed to search reduction of carbon emissions, mitigation climate change, support the transition to low-carbon company and promote sustainability. Researchers think about how companies can evaluate their carbon footprint considering carbon policies. So, the conception of a green supply chain represents one of environmental impact strategy for societies. The objective of our study is the assessment of the effect of the implementation of green practices on the supply chain management such as: the green procurement incentive policy, the collection and recovery of returned product and the carbon footprint assessment policies. Therefore, we develop a new multi objective model aiming the design of a green closed loop supply chain with carbon taxation policy consideration. The goal of the suggested approach is to simultaneously minimize the total costs of supply chain activities and the carbon emission. Finally, to test the applicability of the framework, a case study is presented. A CO2 emission limit is defined and beyond this limit, a penalty applies. Simulation results show the existent trade-offs between two dimensions of sustainability.