A learning-based face hallucination method is proposed in this paper for the reconstruction of a high-resolution face image from a low-resolution observation based on a set of high- and low-resolution training image pairs. The proposed global linear modal based super-resolution estimates the optimal weights of all the low-resolution training images and a high-resolution image is obtained by applying the estimated weights to the high-resolution space. Then, we propose a position based local residue compensation algorithm to better recover subtle details of face. Experiments demonstrate that our method has advantage over some established methods.