Tube spinning is an effective plastic-forming technology for forming light-weight, high-precision and high-reliability components in high-tech fields, such as aviation and aerospace. However, cracks commonly occur in tube spinning due to the complexity of stress state, which severely restricts the improvement of the forming quality and forming limit of components. In this study, a finite element (FE) model coupled with Gurson-Tvergaard-Needleman (GTN) damage model for forward tube spinning of 3A21-O aluminum alloy is established and its applicability is evaluated by experiment. Meanwhile, the GTN damage model is employed to study the damage evolution for forward tube spinning of 3A21-O aluminum alloy. The results show that the FE model is appropriate for predicting the macroscopic crack appearing in uplift area for forward tube spinning, while the damage evolution in deformation area could not be predicted well due to the negative stress triaxiality and the neglect of shear deformation. Accumulation of damage in forward tube spinning occurs mainly in the uplift area. Void volume fraction (VVF) in the outer surface of the tube is higher than that in the inner surface. In addition, it is prone to cracking in the outer surface of tube in the material uplift area.