Environmental protection and sustainable development have become the consensus of all countries in the world. Enterprises must pay attention to the impact on the environment in their operations. Therefore, the selection of green suppliers has become a crucial issue for companies. Supplier selection is a dynamic and complex multi-attribute group decision-making process. The decision results have the tripartite characteristics of “accepted”, “rejected” and “pending further investigation”, and experts need to constantly negotiate in the decision-making process to achieve consensus. In view of the above characteristics, this study constructs a sequential group three-way decision making (TWDM) method to support green supplier selection. Firstly, we review the existing literature on the evaluation criteria and selection methods of green suppliers. In this process, we construct an evaluation attribution system including the following four aspects: product formation, service level, development capability, and green level. Secondly, combining with the sequential and group characteristics of decision making, we propose a multiple-attribute sequential group TWDM method based on a multi-level granularity structure. The weight of each decision maker is determined by his influence weight and interval-valued intuitionistic fuzzy entropy weight. The attribute weight is determined by entropy weight and subjective weight. By using the VIsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method improved by grey relation analysis (GRA), we calculate conditional probabilities. Since the cumulative prospect theory can reflect the risk attitude of decision makers, we apply it to calculate the decision thresholds. Finally, we apply a case of Q automobile manufacturer to verify the effectiveness, applicability and feasibility of the method. The innovation of this study is to construct social networks at each granularity level and introduce an expert information exchange model to promote group consensus. The sequential group TWDM method provides a new reference and idea for the selection of green suppliers.