Nowadays, increasing awareness of environmental protection has evoked the adoption of green technologies in design and manufacturing. As a revolutionizing manufacturing technology that produces components in a layer-by-layer fashion, Additive Manufacturing (AM) has followed this trend. Among variety of AM processes, Fused Filament Fabrication (FFF) is one of the most commonly used technology. However, AM (including FFF) is inherently energy expensive and energy inefficient compared with conventional manufacturing. Thus, an urgent investigation is needed to reduce the energy consumption. On the other hand, part geometric accuracy is an important aspect for the quality. It is not meaningful to improve AM's energy consumption performance with compromised part geometric accuracy. Therefore, it is necessary to jointly consider energy consumption as well as part geometric accuracy in the AM process design. This study applies the statistical regression approach to model AM energy consumption and part geometric accuracy. The non-dominated sorting genetic algorithm II (NSGA-II) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method together are used to locate the compromised optimal solution for AM process parameter settings. The effectiveness of proposed approach is demonstrated through a case study developed with FFF process and a specific part design. The results of this study are significant to both AM energy consumption and part geometric accuracy in terms of qualitative and quantitative analysis. Furthermore, the study can potentially guide the future AM sustainability model development and to be extended to future AM process improvement.