In this paper, we study face hallucination or synthe-sizing a high-resolution face image from a low-resolution input, with the help of a large collection of other high-resolution face images. We develop a two-step statistical modeling approach that integrates both a global parametric model and a local nonparametric model. First, we derive a global linear model to learn the relationship between the high-resolution face images and their smoothed and down-sampled lower resolution ones. Second, the residual between an original high-resolution image and the reconstructed high-resolution image by learned linear model is modeled by a patch-based nonparametric Markov network, to capture the high-frequency content of faces. By integrating both global and local models, we can generate photo-realistic face images. Our approach is demonstrated by extensive experiments with high-quality hallucinated faces.