A closed-loop supply chain (CLSC) is important in developing a green industrial supply chain and a sustainable economy. This study addresses the challenge of designing a closed-loop supply chain network (CLSCN) under demand uncertainty by integrating forward and reverse logistics. A continuous approximation (CA) approach is proposed to solve a responsive CLSCN model. An inventory-sharing strategy is applied in the continuous approximation (CA) approach to further solve uncertain demand in a CLSCN. We conduct sensitivity analysis to demonstrate how the optimal design characteristics and the responsive supply chain network (SCN) design depend on various scenarios. A responsive CLSCN's network density is higher than a responsive SCN's. The changes in network density of the distribution center (DC) are not significantly affected by increased risks of uncertainties. The proposed model has demonstrated substantial cost savings compared to the traditional responsive CLSCN model.