Recently, sustainable supply chain management (SSCM) has become one of the important subjects in the industry and academia. Supplier selection, as a strategic decision, plays a significant role in SSCM. Researchers use different multi-criteria decision making (MCDM) methods to evaluate and select sustainable suppliers. In the previous studies, evaluation is solely based on the desirable features of suppliers and their risks are neglected. Therefore, current research uses failure mode and effects analysis (FMEA) as a risk analysis technique to consider supplier's risk in combination with the MCDM method. Practically, this study operated in two main stages. In the first stage, the score of the suppliers obtains by integration Fuzzy MOORA and FMEA. In the second stage, the output of the previous stage used as input parameters in developed mix-integer linear programming to select suppliers and order optimum quantity. Finally, to demonstrate the effectiveness of the proposed approach, a case study in a chemical industry and sensitivity analysis is presented.