The mechanical properties, texture transformation, and mechanism of Al–Cu–Mn alloy during annealing were studied using three-dimensional orientation distribution function (ODF), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM). The results showed that the increase in yield strength after annealing at 200 °C is due to the decrease in the proportion of P and M textures and the increase in the proportion of Goss texture. The increase in the change rate of mechanical properties observed during annealing at 250 and 350 °C can be attributed to the higher proportion of M and P textures and the reduced proportion of Goss textures. Among them, the proportion of M texture increased significantly, and the Goss texture decreased significantly after annealing at 350 °C. This is because the structural energy density (Ev) value of the Goss texture is higher than that of the M texture at 250 °C and 350 °C. The Goss texture is in an unstable state of high energy order. The deformed Goss texture is unstable at high temperatures, leading to conversion into M and other textures. The EBSD and TEM analysis revealed that the hardness is mainly related to the change in dislocation density. When the annealing temperature is increased from 250 to 350 °C, the hardness is significantly reduced from 62 HV to 52 HV, and the dislocation density is reduced from 4.0 × 1014 ρ/m−2 to 2.4 × 1014 ρ/m−2.