In the present study, tungsten inert gas wire and arc additive manufacturing was used to process an iron-based FeMnAlNi shape memory alloy. By a layer-by-layer method, a wall structure with a length of 60 mm and a height of 40 mm was generated. Bidirectional welding ensured grain growth parallel to the building direction. To maintain a nearly constant temperature–time path upon cooling, the structure was fully cooled after each weld to room temperature (298 K). With this approach, an anisotropic microstructure with a grain length of up to 8 mm (major axis) could be established. The grain morphology and formed phases were investigated by optical microscopy and scanning electron microscopy. The images revealed a difference in the orientation with respect to the building direction of the primarily formed γ grains along the grain boundaries and the secondarily formed γ grains in the heat-affected zones. Subgrains in the α matrix were observed also by scanning electron microscopy. With X-ray diffraction, the preferred orientation of the α grains with respect to the building direction was found to be near ⟨100⟩. Overall, an anisotropic polycrystalline material with a columnar texture could be produced, with a preferred grain orientation promising high values of transformation strains.