Evaluating and selecting appropriate sustainable supplier is regarded as a significant decision thatplays a main role to successfully manage the sustainable supply chain. This study introduces a novelinterval-valued fuzzy group decision model for evaluating sustainability performance of suppliersin the sustainable supply chain management (S-SCM). For this purpose, values of two high possibil-isic mean and low possibilistic standard deviations are presented to provide new separation mea-sures matrixes. Then, new interval-valued fuzzy indexes are proposed based on concepts of fuzzypossibilistic statistical reference point system. In addition, evaluation criteria from sustainable devel-opment dimensions are considered along with the conventional criteria for comprehensive assess-ment approach. Steps of the proposed interval-valued fuzzy group decision model are implementedto a case study in the supply chain for the sustainable supplier selection problem. The computa-tional results of the presented model are compared with two recent fuzzy decision methods fromthe related literature. The model can assist supply chain experts or decision-makers to systematicallydetermine preference order of sustainable supplier candidates under uncertain conditions.