The gyroid is a triply periodic minimal surface (TPMS) that efficiently distributes stress under compressive loading in all Cartesian orientations. Despite the gyroid’s geometric ability to evenly distribute load, it has yet to be more broadly introduced to concrete additive manufacturing (AM) due to the difficulty of printing steep, doubly curved overhangs with a cementitious material. Consequently, the employment of the gyroid TPMS in AM has been limited to small and nano-scale applications. However, for doubly curved 3D printed concrete (3DPC) structures, the feasibility of the print is determined by the relationship between geometry, tool path design, and the mechanical and rheological properties of the concrete material being extruded. Using a 6-axis robotic arm with an accelerator-injection extruder as an end-effector, this research examines the fabrication limitations to construct a 3DPC gyroid. Finally, one of the overhang samples was prepared for a series of compression tests, which demonstrated that the 3DPC gyroid structure could support over 1000 kilonewtons. Though large variability was observed in the performance of the three gyroid samples tested, the research demonstrates that steep overhangs can be printed in concrete for gyroid-based structures.