Abstract: With the rapid development of convolutional neural networks, deep learning has been widely used in the field of face recognition. In recent years, the accuracy of face recognition has increased rapidly, mainly due to the proposition of novel loss functions. On the current largest face test set MegaFace, the top model has achieved 97.91% 1∶N search performance, but the problem of convergence stability during training has not been properly solved. Thus a new type of loss function, Lineface, is proposed in this paper. Its logic curve is linear in the cosine space, which makes the gradient convergence better and more stable during training. A large number of experiments show that good model performance and convergence can be achieved.