As a forming process with less mold constraints, free bending technology is prone to the occurrence of wrinkling defects caused by instability of thin-walled tubes, which limits its application in high-end manufacturing fields. This study establishes a mechanical model for unstable wrinkling of AA5052 aluminum alloy thin-walled tubes used in aerospace vehicles. Theoretical analysis indicates that the initial geometric micro-defects in the tubes significantly reduce the forming limit under influence of the additional axial thrust. In addition, the mechanical properties of AA5052 aluminum alloy tubes were obtained through uniaxial tensile tests. On the basis of considering initial geometric micro-defects, a finite element model for predicting wrinkling during coreless free bending forming of AA5052 tubes was established using the ABAQUS/Implicit algorithm. The results indicate that the simulation prediction model incorporating initial geometric micro-defects can effectively predict the geometric shape and development trend of tube wrinkling. Finally, accuracy of the model was verified through free bending forming tests. This study is of great significance for understanding the unstable wrinkling behavior in free bending forming and improving the control level in manufacturing process.