The effect of texture on the anisotropy of tensile properties of the SLM‐formed and annealed Ti6Al4VE alloy is investigated. The component of microstructure in these alloys is dominated by the α/α′ phase. Furthermore, there is a significant difference in the intensity of X‐ray diffraction peaks between the XY plane that is perpendicular to the build direction (BD) and the XZ plane that is parallel to the BD, though alloys are annealed with the same treatment. Ultimate tensile strength and yield strength in the X direction are higher than in the Z direction and exhibit significant anisotropy in the alloy annealed with the same treatment conditions, but the plasticity presents an opposite trend. The average Schmid factor of the basal <α>, prismatic <α>, and pyramidal slip systems in the alloy is analyzed by electron backscatter diffraction and presents that the prismatic <α> slip is the main deformation mode during the tensile testing. The <0001> fiber texture parallel to the loading direction in the XY plane is stronger than that in the XZ plane and causes a decrease in the number of the basal <α> slip system activating in the XY plane in contrast to the XZ plane.