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Due to increasing air pollution, which is a consequence of the environmental effects of production in various industries, green supply chain management (GSCM) has attracted the attention of both scholars and practitioners. Green supplier selection is an important problem in GSCM and seeks to satisfy a firm's environmental goals as well as its economic targets. In this paper, for the first time, a green supplier selection problem considering both green and non-green evaluation criteria in a closed-loop supply chain is studied, and a cap-and-trade mechanism as a way of controlling the air pollution caused by manufacturers is proposed. To solve this particular problem, we propose a multi-objective robust optimization (RO) model. This specific model is an effective approach to handle uncertainty. A numerical example using randomly generated data, accompanied by subsequent discussion of the proposed approach, is deployed to validate the model. The results prove that the developed model for green supplier selection is able to effectively enhance the decision-making process of the experts. By illustrating the trade-off in robustness between the model and proposed solutions, as well as the effect of the deviation penalty on the closeness of results to the achieved solution, we show how firms can make optimal decisions when assigning the parameters. Furthermore, analyses show that decreasing the allowance amount (cap) and increasing the allowance prices in the cap-and-trade system escalate the firms' costs, but lower the amount of carbon released. Finally, we show that the cap-and-trade mechanism results in a better solution in terms of the total utility of the supply chain compared to the penalty-based system for a specific range of carbon allowance. • This paper generalizes the green supplier selection and order allocation problem. • A mathematical model for the problem is developed. • A robust optimization approach to handle the model uncertainty is developed. • The impact of changes in model parameters on the objective functions is analyzed. • The cap-and-trade mechanism is compared with a penalty-based mechanism. [ABSTRACT FROM AUTHOR]