In recent years, various organizations have focused on considering the sustainability concept in the supply chain (SC) design. Managers try to increase the sustainability of SCs to achieve a competitive advantage in today’s growing market. Designing a sustainable supply chain (SSC) by integrating economic, social, and environmental dimensions affects the SC’s overall performance. To achieve the SSC, decision makers (DMs) are required to evaluate different strategies and then apply the most effective one to design SC networks. This study proposes an assessment approach based on the network data envelopment analysis (DEA) to choose an efficient strategy for each stage of an SSC network. This approach seeks to provide a sustainable design with DMs to avoid imposing additional costs on SCs that result from noncompliance with environmental and social issues. To this end, we consider sustainability-concept-related inputs and outputs in the network DEA model to choose the most efficient strategy for SSC design. The strategy selection process can become an important issue, especially when SCs active in a competitive environment. Accordingly, a crucial feature of the presented model is considering the issue of competition to choose the efficient strategy. Furthermore, undesirable outputs and feedbacks and independent inputs and outputs for intermediate stages in the network system are considered to create a structure compatible with the real world. The output of the proposed approach enables DMs to select the appropriate strategy for each stage of the SSC network to maximize the aggregate efficiency of the network.