Dataset for paper entitled, 'Tailoring equiaxed ��-grain structures in Ti-6Al-4V coaxial electron beam wire additive manufacturing'. Abstract: High-deposition-rate, directed-energy-deposition additive manufacturing (DED-AM) processes typically produce Ti-6Al-4V (Ti64) components with coarse columnar ��-grain structures that lead to undesirable mechanical anisotropy, as well as a fine heterogeneous lamellar transformation microstructure, which is very different to that seen standard wrought products. This arises because of the intrinsic lack of constitutional undercooling at the solidification front, and the subsequent high cooling rates and rapid thermal cycling experienced by the deposited material. In this work, the more refined primary ��-grain solidification structures and textures seen in components built with the novel coaxial electron beam wire DED AM (CEWAM) process have been characterised in detail, for the first time, with the aim of investigating the potential for this technology to directly replicate the ��-annealed damage-tolerant microstructure used in large Ti64 aerospace forgings. Due to its different lower energy density solidification conditions, it has been confirmed, by electron backscatter diffraction (EBSD) analysis and ��-grain reconstruction in three orthogonal cross-sections, that the CEWAM process changes the melt conditions to promote ��-grain nucleation ahead of the solidification front, which can result in a highly refined, equiaxed, ��-grain structure. However, the conditions for refinement were marginal and a mixed grain structure was commonly observed in thicker sections. Additionally, the subsequent grain-growth stability during ��-annealing was investigated. It is shown that an equivalent microstructure can be achieved to that seen in a standard ��-forged component, by grain structure homogenisation and slow cooling through the �� transus, to promote �� colony nucleation, allowing direct part substitution. This was made possible by the refined primary ��-grain structure achieved during deposition with the CEWAM solidification conditions which, importantly, are also shown to lead to a weaker texture than in a typical forging. Paper doi: https://doi.org/10.1016/j.mtla.2021.101202