Against the backdrop of responsible economic development, sustainable supply chain management (SSCM) is key to achieving the sustainable development for enterprise and industry. In this regard, sustainable supplier selection is crucial in SSCM. By integrating the three dimensions of sustainability, economic, environmental and social, this paper presents a new evaluation system for supplier selection from a sustainability perspective. Specifically, we design a decision mechanism for sustainable supplier selection based on linguistic 2-tuple grey correlation degree. In this proposed mechanism, the hybrid attribute values whereby real numbers, interval numbers and linguistic fuzzy variables coexist are transformed into linguistic 2-tuples. A ranking method based on linguistic 2-tuple grey correlation degree is then presented to rank the suppliers. An application example is presented to highlight the implementation, availability and feasibility of the proposed decision making mechanism.