This paper proposes a novel method for recognizing faces degraded by blur using deblurring of facial images. The main issue is how to infer a Point Spread Function (PSF) representing the process of blur on faces. Inferring a PSF from a single facial image is an ill-posed problem. Our method uses learned prior information derived from a training set of blurred faces to make the problem more tractable. We construct a feature space such that blurred faces degraded by the same PSF are similar to one another. We learn statistical models that represent prior knowledge of predefined PSF sets in this feature space. A query image of unknown blur is compared with each model and the closest one is selected for PSF inference. The query image is deblurred using the PSF corresponding to that model and is thus ready for recognition. Experiments on a large face database (FERET) artificially degraded by focus or motion blur show that our method substantially improves the recognition performance compared to existing methods. We also demonstrate improved performance on real blurred images on the FRGC 1.0 face database. Furthermore, we show and explain how combining the proposed facial deblur inference with the local phase quantization (LPQ) method can further enhance the performance.