Learning the discriminative features of different faces is an important task in face recognition. By extracting face features with neural networks, it becomes easy to measure the similarity of different face images, which makes face recognition possible. To enhance a neural network's face feature separability, incorporating an angular margin during training is common practice. The state-of-the-art loss functions CosFace and ArcFace apply fixed margins between the weights of classes to enhance the inter-class separation of face features. Since the distribution of samples in the training set is uneven, the similarities between different identities are unequal. Therefore, using an inappropriately fixed angular margin may lead to problems such as that the model has difficulty converging or that the face features are not sufficiently discriminative. It is more intuitive to use adaptive angular margins are angular adaptive, which can increase as the angles between classes increase. In this paper, we propose a new angular margin loss named X2-Softmax. X2-Softmax loss has adaptive angular margins, which increase as the angle between different classes increases. The angular adaptive margin ensures model flexibility and effectively improves the effect of face recognition. We trained a neural network with X2-Softmax loss on the MS1Mv3 dataset and tested it on several evaluation benchmarks to demonstrate the effectiveness and superiority of our loss function.