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In this paper, an efficient feature extraction technique called Local Graph Embedding Discriminant Analysis (LGEDA) is developed for solving one sample per person problem. In our algorithm, a mean filter is used to generate imitated images and a double size new training set can be obtained. Taking the local neighborhood geometry structure and class labels into account, the proposed algorithm can maximize the local interclass separability as far as possible and preserve the local neighborhood relationships of the data set. After the local scatters and interclass scatter are characterized, the proposed method seeks to find a projection maximizing the local margin between of different classes under the constraint of local neighborhood preserving. Experiments show that our proposed method consistently outperforms some other state-of-the-art techniques.