The objective of this paper is to develop an approach based on the Taguchi method with Fuzzy grey relational analysis (F-GRA) for process parameters optimization of green EDM which reflects the manufacturing priority between environmental and machining factors. A grey relational grade obtained from the grey relational analysis is used to optimize the process parameters. In this research, initially, Taguchi experimental technique was used to perform the experiments and, thereafter F-GRA were developed to solve the multi-response process parameters optimization problem. Computation of weight associated with each of the output parameters were done using triangular fuzzy numbers (TFN). Finally; the ranking of the parameters is prepared based on the conversion of the multiple responses into single response analysis using GRA methodology. The sensitivity analysis also has been carried out to demonstrate the impact of the distinguishing coefficient on the result of GRA. An attempt was made to compare the proposed methodology with the Fuzzy-TOPSIS and Taguchi-VIKOR methodology. The result shows that F-GRA outperforms the other existing methodology. A case study on EDM has been presented to justify the proposed model for sustainable manufacturing process.