This paper focuses on the construction and optimization of neighbour graph and proposes a Supervised Graph-optimized Locality Preserving Projections (SGoLPP) method for facial feature extraction. Different from the Locality Preserving Projections(LPP) that it predefines the weight matrix and solves the projection matrix by one step optimization,the SGoLPP incorporates the weight matrix into the objective function as a learning term, and optimizes the weight matrix and projection matrix simultaneously. Meanwhile, the label information is utilized to update the weights corresponding to sample pairs in the same class and to avoid the interferences from samples not in the same class. Experiments on the Wine database of UCI show that the SGoLPP achieves better cluster performance with less iterations. For face recognition, the average recognition accuracies of SGoLPP on Yale, UMIST and CMU PIE face databases are 26.6%, 4.8% and 8.8% higher than those of LPP, Supervised Locality Preserving Projections(SLPP) and Graph-optimized Locality Preserving Projections(GoLPP), respectively, which verifies the effectiveness and superiority of the proposed method.