During the last decades, the use of additive manufacturing techniques has revolutionized the fabrication of mechanical parts and enabled the reliable creation of complex geometries using various types of materials. In the case of thermoplastic polymers, Fused Filament Fabrication (FFF) process is a common choice and based on a favorable regulation of its parameters, an appropriate compromise between different objectives can be reached. In this work, experiments designed according to Taguchi L9 orthogonal array were carried out and after statistical analysis of the results, the optimization of FFF printing process of poly (ethylene terephthalate glycol-modified) (PETG) parts was performed based on multiple objectives such as compressive mechanical strength, part weight and printing time, in respect to process parameters such as infill density, infill pattern and layer height. After the experimental results of compression tests were analyzed, Grey Relational Analysis (GRA) method was applied to determine the optimum printing parameters. The findings indicate that the use of hexagonal infill pattern, high infill density and layer height can lead to both relatively high mechanical properties and low printing time.