A box-shaped Ti–6Al–4V alloy part was fabricated by laser powder bed fusion (LPBF) with a gas-atomized powder and annealed at 800 °C for 2 h. The defects, microstructures and mechanical properties of the part at different distances from the substrate and in different directions were studied. It was found that the part contained blowhole defects and exhibited a columnar macrostructure of prior β grains with a microstructure mixed by α variant colony and basketweave microstructure. The prior β grains and α lamellae near the substrate were coarser due to preheating impeding heat transfer and they were slightly finer in the last solidified layers and the heat-affected zone due to incomplete in-situ heat treatment, and this rendered the latter to have better ductility than the former (elongation to fracture 11.1% vs. 8.1%) without changing the strength (yield strength: 961 MPa, ultimate tensile strength: 1042 MPa). The box-shaped part exhibited anisotropy of mechanical properties due to the columnar macrostructure and the α phase preferred orientation that activates a higher proportion of prismatic <a> slips.