Linear discriminant analysis （ LDA） can only make use of labeled samples. In order to overcome this shortcoming,a new semi-supervised discriminant analysis method based on local reconstruction and global preserving marked as LRGPSSDA is proposed. LRGPSSDA sets the edge weight of neighborhood graph by minimizing the local reconstruction error and preserves the global geometric structure of the sampled data set without destroying its local geometric structure. It is insensitive to the selection of neighborhood parameter,and the dimensionality of its projection subspace is independent of the number of sample classes. As compared with the existing semi-supervised discriminant analysis methods such as SDA and UDA,LRGPSSDA is of higher classification performance. The experimental results of YaleB and CMU PIE face database also demonstrate that LRGPSSDA is effective.