Face recognition has been well studied under visible light and infrared (IR) in both intra-spectral and cross-spectral cases. However, how to fuse different light bands for face recognition, i.e., hyperspectral face recognition, is still an open research problem, which has the advantages of richer information retention and all-weather functionality over single-band face recognition. Thus, in this research, we revisit the hyperspectral recognition problem and provide a deep learning-based approach. A new fusion model (named HyperFace) is proposed to address this problem. The proposed model features a pre-fusion scheme, a Siamese encoder with bi-scope residual dense learning, a feedback-style decoder, and a recognition-oriented composite loss function. Experiments demonstrate that our method yields a much higher recognition rate than face recognition using only visible light or IR data. Moreover, our fusion model is shown to be superior to other general-purpose image fusion methods that are either traditional or deep learning-based, including state-of-the-art methods, in terms of both image quality and recognition performance.