Typically, the deployment of face recognition models in the wild needs to identify low-resolution faces with extremely low computational cost. To address this problem, a feasible solution is compressing a complex face model to achieve higher speed and lower memory at the cost of minimal performance drop. Inspired by that, this paper proposes a learning approach to recognize low-resolution faces via selective knowledge distillation. In this approach, a two-stream convolutional neural network (CNN) is first initialized to recognize high-resolution faces and resolution-degraded faces with a teacher stream and a student stream, respectively. The teacher stream is represented by a complex CNN for high-accuracy recognition, and the student stream is represented by a much simpler CNN for low-complexity recognition. To avoid significant performance drop at the student stream, we then selectively distil the most informative facial features from the teacher stream by solving a sparse graph optimization problem, which are then used to regularize the finetuning process of the student stream. In this way, the student stream is actually trained by simultaneously handling two tasks with limited computational resources: approximating the most informative facial cues via feature regression, and recovering the missing facial cues via low-resolution face classification. Experimental results show that the student stream performs impressively in recognizing low-resolution faces and costs only 0.15MB memory and runs at 418 faces per second on CPU and 9; 433 faces per second on GPU.