A growing number of companies treat "sustainability" as an important objective in their strategy. Sustainable and green suppliers increase efficiency by reducing costs and waste in industries. Sustainable and green supplier selection is a critically important factor in moving forward along the path of sustainability. A fuzzy R-method is proposed in this paper based on ranking the fuzzy numbers of alternative suppliers and criteria. Triangular fuzzy membership function and different fuzzy scales are presented to demonstrate and validate the proposed method. Fuzzy composite scores are generated, and these scores are converted into crisp forms to evaluate the alternative suppliers. The novelty of the proposed method is that it is simple, can deal with qualitative and quantitative criteria of supplier selection, and requires less computational effort for evaluating and ranking the green and sustainable suppliers in fuzzy group decision-making situations. The weights of the criteria and alternative suppliers are generated using a simple equation and hence there is no need to apply different methods for weights generation and ranking. Furthermore, this method does not require normalization of the data. Two realistic group decision-making problems of green and sustainable supplier selection to test the method. Sensitivity analysis for the proposed method is also conducted to check the consistency of the proposed method to different weights of the criteria. The proposed method is effective, robust, and competitive to the existing multi-criteria decision making (MCDM) methods of sustainable supplier selection.