In the existing face hallucination approach using Locality Preserving Projections (LPP), the weight in neighborhood graph is artificially predefined, and this scheme does not benefit for subsequent learning process. That may bring about some uncertainty situation in the performance of algorithm. In this paper we use a novel dimension reduction algorithm called Graph-optimized Locality Preserving Projections(GoLPP), which takes construction of neighborhood graph in a optimal way. Then, Generalized Regression Neural Network (GRNN) is used to predict the global high resolution face image. However, the face image obtained by GRNN is smooth and lack of high frequency information. To enhance the image visual quality, a patch based Residual model is adopted. Experiment results show that the proposed approach can reconstruct high resolution face image efficiently, and the performance is better than other methods based LPP.