In this letter, we propose a novel method for face hallucination by learning a new distance metric in the low-resolution (LR) patch space (source space). Local patch-based face hallucination methods usually assume that the two manifolds formed by LR and high-resolution (HR) image patches have similar local geometry. However, this assumption does not hold well in practice. Motivated by metric learning in machine learning, we propose to learn a new distance metric in the source space, under the supervision of the true local geometry in the target space (HR patch space). The learned new metric gives more freedom to the presentation of local geometry in the source space, and thus the local geometries of source and target space turn to be more consistent. Experiments conducted on two datasets demonstrate that the proposed method is superior to the state-of-the-art face hallucination and image super-resolution (SR) methods.