Nowadays, increasing number of companies incorporates the reverse logistics decisions into their supply chain design in order to cope with the enforced international and national legislation and improve the resource efficiency and public image. This paper investigates a new stochastic optimization model for designing a single-period multi-product multi-level reverse logistics system under government subsidy and low-carbon emission requirement. In order to resolve the stochastic optimization problem, a modified multi-criteria scenario-based approach is proposed to maximize the profit generation while simultaneously improve the stability of the decision-making under uncertainty. The model and solution method are tested with several numerical experiments, and managerial insights are obtained with respect to the carbon emission requirement, governmental subsidy, economy of scale, and system flexibility.