In this paper, we propose a novel face hallucination method to reconstruct a high-resolution face image from a lowresolution observation based on a set of high- and lowresolution local training image pairs. Instead of basing on probabilistic or manifold learning models, the proposed method synthesizes the high-resolution image patch using the same position image patches of training image pairs. A cost function is formulated to obtain the optimal weights of the training image position-patches and the high-resolution patches are reconstructed using the same weights. The final high-resolution facial image is formed by integrating the hallucinated patches. Experiments show that the proposed method without residue compensation generates higherquality images than some methods.