Fierce competition in the market has forced companies to study their supply chain networks more. Due to increased social awareness and stricter governmental laws and legislation, the green closed-loop supply chain (GCLSC) has been reviewed more recently. The main goal of this study is to propose a multi-objective model for optimization of a comprehensive green closed-loop supply chain network with a multi-period multi-stage network, including the manufacturer, distributor, customer market, collection, recovery, and disposal centers under uncertain demand. To handle the uncertain parameter, we utilized chance constraint fuzzy programming. We considered different objective functions, consisting of maximizing income, minimizing total supply chain cost, and minimizing total CO₂ emissions (i.e., CO₂ emitted from facility centers and various transportation modes). Aimed at achieving optimal values, we utilized a carbon-pricing approach to transform the problem into a single objective function. A numerical example coupled with a sensitivity analysis has been conducted to validate the proposed model and formulation. The results show the suitability of the model and the formulation.