Additive Manufacturing (AM), specifically Fused Deposition Modeling (FDM), has become a highly promising method for creating intricate shapes using different materials. Polyethylene Terephthalate Glycol (PETG) is a highly utilized thermoplastic that is recognized for its exceptional strength, resistance to chemicals, and effortless processing. This study aims to optimize the process parameters of the FDM technique for PETG material using Taguchi Grey Relational Analysis (GRA). An empirical study was carried out to examine the impact of various FDM process parameters, such as layer thickness, infill density, printing speed, and nozzle temperature, on important outcome variables like dimensional accuracy, surface quality, and mechanical properties. The Taguchi method was used to systematically design a series of experiments, while GRA was used to optimize the process parameters and performance characteristics. The results unveiled the most effective parameter combinations for attaining exceptional printing quality and mechanical properties of PETG parts. Furthermore, Grey Relational Grades helped to identify the key factors that affect the performance of the AM process. This study enhances the progress of additive manufacturing methods, particularly Fused Deposition Modeling (FDM), for PETG material. It focuses on meeting the increasing need for efficient and affordable production in diverse industries such as aerospace, automotive, and medical sectors. This study utilizes Taguchi Grey Relational Analysis to offer valuable insights into parameter optimization strategies that can be applied to a wide variety of additive manufacturing applications.