Abstract: Conventional appearance-based face recognition needs to convert the image matrix into a higher dimensional vector. This will aggravate ``the curse of dimensionality'' problem and small sample size problem for those who adopt Fisher discriminant criterion. Moreover, existing feature extractions based on tensor (matrix) representation of image encounter the problem that dimensionality of extracted feature is still too high or there is no convergent solution. Based on matrix representation of image and matrix bidirectional projection, a novel feature extraction method called MMC-MBP (maximum margin criterion and image matrix bidirectional projection) for face recognition is proposed. On the one hand, since the Laplacian matrix, which can preserve the locality of the data set, has been introduced into the scatter matrix, MMC-MBP can preserve the intrinsic manifold structure of face set. On the other hand, MMC-MBP adopts an efficient and stable maximum margin criterion, so it can conquer the small sample size problem brought by Fisher discriminant criterion. What is more, an iterative procedure, which is proven to be convergent and can monotonously increase the objective value, is devised to compute the optimal projection matrices. Thus, the proposed MMC-MBP approach can conquer the problem of existing tensor (matrix) projection based feature extraction approaches. Extensive and systematic experiments on CMU PIE face database and Yale face database verify the high convergence speed of the iterative solution procedure and demonstrate that the proposed MMC-MBP outperforms the state-of-the-art methods in face feature extraction such as Eigenfaces, Fisherfaces, and Laplacianfaces.