Academics' and practitioners' interest in sustainable supply chain management has received great concern in recent years. The application of biaxially-oriented polypropylene (BOPP) plastic film has had a significant influence on the economic, environmental and social performance of supply chain management. However, research on the integration of these three sustainable dimensions is still rare in this field. In this paper, we identify sustainability criteria based on a triple bottom line approach (economic benefit, environmental protection and social responsibility) from the supply chain perspective, develop a hybrid multi-criteria decision making framework to evaluate the criteria and select alternatives and apply the proposed approach to a real case study at a focal BOPP plastic film company in China. In the framework, a fuzzy analytical hierarchy process (FAHP) is used to determine the performance criteria weights and a fuzzy technique for order performance by similarity to ideal solution (FTOPSIS) is applied to rank the alternatives. The case study finds that the economic dimension was the most important aspect with environmental second and social third. The results also verify the effectiveness of the proposed framework. This paper develops an effective and systematic approach for decision makers to conduct evaluations and select optimal alternatives for focal plastic film companies.