Locality Preserving Projection (LPP) has shown great efficiency in feature extraction. LPP captures the locality by the K-nearest neighborhoods. However, recent progress has demonstrated the importance of global geometric structure in discriminant analysis. Thus, both the locality and global geometric structure are critical for dimension reduction. In this paper, a novel linear supervised dimensionality reduction algorithm, called Locality and Global Geometric Structure Preserving (LGGSP) projection, is proposed for dimension reduction. LGGSP encodes not only the local structure information into the optimal objective functions, but also the global structure information. To be specific, two adjacent matrices, that is, similarity matrix and variance matrix, are constructed to detect the local intrinsic structure. Besides, a margin matrix is defined to capture the global structure of different classes. Finally, the three matrices are integrated into the framework of graph embedding for optimal solution. The proposed scheme is illustrated using both simulated data points and the well-known Indian Pines hyperspectral data set, and the experimental results are promising.