Energy resulting from an impact is manifested through unwanted damage to objects or persons. New materials made of cellular structures have enhanced energy absorption (EA) capabilities. The hexagonal honeycomb is widely known for its space-filling capacity, structural stability, and high EA potential. Additive manufacturing (AM) technologies have been effectively useful in a vast range of applications. The evolution of these technologies has been studied continuously, with a focus on improving the mechanical and structural characteristics of three-dimensional (3D)-printed models to create complex quality parts that satisfy design and mechanical requirements. In this study, 3D honeycomb structures of novel material polyethylene terephthalate glycol (PET-G) were fabricated by the fused deposition modeling (FDM) method with different infill density values (30%, 70%, and 100%) and printing orientations (edge, flat, and upright). The effectiveness for EA of the design and the effect of the process parameters of infill density and layer printing orientation were investigated by performing in-plane compression tests, and the set of parameters that produced superior results for better EA was determined by analyzing the area under the curve and the welding between the filament layers in the printed object via FDM. The results showed that the printing parameters implemented in this study considerably affected the mechanical properties of the 3D-printed PET-G honeycomb structure. The structure with the upright printing direction and 100% infill density exhibited an extension to delamination and fragmentation, thus, a desirable performance with a long plateau region in the load–displacement curve and major absorption of energy.