This paper investigates a predictive algorithm for the angle of the metal tube-bending rebound with small samples. First, the generative adversarial network (GAN) approach is introduced to address the issues of insufficient sample data. The proposed method can realize data augmentation through a generator, enhancing training effectiveness compared to conventional model-based and experimental prediction methods. To further reduce the problems caused by the small samples, the Wasserstein distance is utilized as the optimization objective for the GAN approach. Second, after obtaining the augmented dataset, Support Vector Regression (SVR) is employed to predict the rebound model of the metal tube-bending. A novel predictive algorithm for the angle of the metal tube-bending rebound based on GAN–SVR is proposed. It exhibits that the GAN–SVR owns more positive prediction ability and error when dealing with small samples than conventional GAN-radial basis function methd (GAN–BP) and GAN–convolutional neural networks. Finally, the effectiveness of the proposed method is validated through experimental results.