With the recent emphasis on supply risk management in sustainable supply chains (SSCs), the evaluation and selection of appropriate suppliers are more important than ever. However, most existing research does not take all three sustainability perspectives of supply risk into account simultaneously and they rarely consider the correlation among supply risk factors in risk assessment. Therefore, considering the uncertain information decision-making environment, this research paper proposes a risk-based integrated group decision-making model for sustainable supplier selection (SSS). First, the weights of decision-makers (DMs) are taken as linguistic terms denoted by intuitionistic fuzzy numbers (IFNs). Second, after obtaining the aggregated intuitionistic fuzzy decision-making matrix considering the expert weights, this study uses the entropy weight method to calculate the criteria weights objectively. Then, the improved failure mode and effects analysis (FMEA) is adopted for the risk assessment to exclude high-risk suppliers. Finally, the extended alternative queuing method (AQM) is applied to rank the qualified suppliers in SSCs. This model can not only enable enterprises to reduce supply risk in SSS practices and identify and prevent the failure modes that lead to supply risk, but also reduce the uncertainty of decision-making, in order to make supplier selection more accurate. The feasibility and effectiveness of the proposed model are illustrated through application in a leading Chinese electrical appliance manufacturing company.