Supplier selection is an important task in supply chain management, as suppliers have a vital role in the success of organisations in a supply chain. Sustainability has emerged as a solution to decreasing resources and increasing environmental and social problems in the past few decades. It has been applied to various industrial operations, one of them is supplier selection, to mitigate unwanted effects in the future. Sustainable supplier selection is a complicated multi-criteria decision making problem, including several criteria from economic, environmental, and social perspectives. To deal with subjective judgements of decision makers, fuzzy and grey methods are widely used in multi-criteria decision making, In the case of small, limited, and incomplete data, the grey theory provides satisfactory results, compared to fuzzy methods. Therefore, this study is an integrated method including grey Best-Worst Method (BWM) and grey Weighted Sum-Product (WISP) for choosing the most sustainable supplier for a textile manufacturer, which includes three main criteria and twelve sub-criteria. According to the result of the proposed model, the supplier with the best performance was determined to be the supplier with the SP2 coded. The results of the developed model were shown to the experts, and the accuracy of the results was confirmed. According to the experts, a higher amount of product can be purchased from the supplier with the SP2 code, and a tighter relationship can be worked with this supplier. The contributions of this study are: (1) Develop a new grey MCDM model called Grey WISP. (2) Create a new integrated MCDM model with grey theory, BWM, and WISP methods that can be applied to assess supplier sustainability using this hybrid model. The proposed model can be used not just for selecting sustainable suppliers, but also for any other decision problems that have multiple criteria and alternatives. The findings suggest that the Grey WISP method achieved accurate results.