A face recognition algorithm based on the angular distance loss function and densely connected convolutional neural network is proposed under the open-set protocol to achieve deep face recognition. The loss function based on angle distance is adopted in the proposed network structure, which makes the facial features more distinguishable and meets the ideal criteria of feature classification. At the same time, the advanced dense connection module is adopted in the proposed neural network structure, which greatly reduces the parameter redundancy of the traditional network structure. After extensive analysis and repeated experiments, the face recognition accuracy reaches 99.45% on the LFW dataset, and the recognition accuracy rates of face identification task and face verification task on MegaFace dataset are 72.534% and 85.34%, respectively. The superiority of the proposed algorithm is confirmed in the face recognition domain.