Due to an increased awareness of ecological protection and resultant stringent legislations, business organizations are highly motivated to improve the sustainable performance of their supply chain in order to achieve sustainable development goals. The chemical industry is a high-risk, high-pollution, and high-efficiency industry, that would benefit from a systematic and sustainability focused evaluation system for supplier selection. Yet, to date, few studies have conducted the necessary in-depth analysis of the characteristics of this industry from the economic, social, and environmental perspectives. Despite the many methods and models that have been proposed to resolve the sustainable supplier selection (SSS) problem, no research has yet considered the different characteristics of each triple bottom line dimension. Accordingly, this paper addresses this problem by proposing a hybrid multi-method and multi-criteria decision-making framework for SSS in the chemical industry. Based on specific characteristics of the chemical industry, this study applies Fuzzy Grey Relational Analysis (FGRA), Failure Mode and Effects Analysis (FMEA), and cloud computing-entropy weight method (EWM) to analyze the economic, social, and environmental dimensions, respectively. Finally, this study integrates the evaluation results of the three dimensions using the Decision-making Trial and Evaluation Laboratory (DEMATEL). The proposed approach and decision-making model can help managers of sustainable supply chains in the chemical industry to choose more sustainable suppliers, respond to market demands quickly, and maintain high competitiveness in the market. An illustrative application of the proposed framework and model is undertaken in one of the biggest Chinese petrochemical companies to verify its practicality and reliability.