Maximum Margin Criterion (MMC) based Feature Extraction method is more efficient than LDA for calculating the discriminant vectors since it does not need to calculate the inverse within-class scatter matrix. However, MMC ignores the discriminative information within the local structures of samples. In this paper, we develop a novel criterion to address the issue, namely Local Maximum Margin Criterion (Local MMC). We define the total laplacian matrix, within-class laplacian matrix and between-class laplacian matrix using the samples similar weighting. Local MMC gets the discriminant vectors by maximizing the difference between between-class laplacian matrix and within-class laplacian matrix. Experiments on FERET face database show the effectiveness of the proposed Local MMC based feature extraction method.