In recent years, concept of sustainability has emerged with increasing awareness of environment-friendly practices and social issues of organizations, researchers, and the business community. For this reason, enterprises have integrated this concept into supply chain management (SCM) by revising on supply chains. In this study, the sustainability concept is combined with the supplier selection process and an integrated approach is proposed to identify best sustainable suppliers. Because of the uncertainties present in individual judgments in sustainable supplier selection (SSS), fuzzy integrated multi-criteria decision making (MCDM) methods are applied in this study. Sustainability criteria are identified from the existing literature and narrowed by NGT (Nominal Group Technique) to build a consensus in group decision-making. A two-stage approach is reported after the identification of criteria and suppliers. In the first stage, the fuzzy Analytic Hierarchy Process (AHP) approach is used to obtain the weights of the SSS criteria and the fuzzy TOPSIS, fuzzy VIKOR and fuzzy MULTIMOORA methods are used to generate the ranking of sustainable suppliers in the second stage. The validity and effectiveness of the proposed approach is illustrated in a foundry manufacturer through a case study. Results show that the three applied fuzzy integrated methods reach similar supplier rankings and the economic perspective between the three dimensions of sustainability is held the first rank.