Presently, environmental management for companies emphasizing environmental protection has become one of the most critical issues for customers, shareholders, governments, employees, competitors, and global pressures requiring organizations to produce environmentally-friendly products and services. This challenge has created a new concept called green supply chain management in business, which combines environmental thinking with the supply chain. Selection of suppliers by considering risk criteria is a category that has attracted the attention of a large number of researchers in order to select the best suppliers according to uncertain factors. In this research, we aim to select a green supplier considering risk factors using a new MCDM approach under uncertainty. For this selection problem, HF-MAIRCA, a new multicriteria sorting method for many alternatives, has been developed. This is used for sorting the alternatives into predefined, ordered supplier categories. This sorting method can be applied to different environmental problems that have a large number of alternatives. As a result of Iran’s case study, the result shows that materials flexibility and materials quality are essential criteria for green supplier selection.