In order to address Small Sample Size (3S) problem encountered by Marginal Fisher Analysis (MFA), based on the maximum margin criterion, a novel algorithm called Maximum Margin Marginal Fisher Analysis (MMMFA) is proposed for supervised linear dimensionality reduction. The difference between similarity matrix which characterizes the interclass separability and similarity matrix which characterizes the intraclass compactness is adopted as discriminant criterion. In such a way, the small sample size problem occurred in MFA is avoided. The relations between MMMFA and conventional linear dimensionality reduction methods such as PCA, LDA and LPP are revealed. Theoretical analysis shows that PCA, LDA and LPP methods could be derived from the MMMFA method. Besides, an efficient and stable MMMFA/QR algorithm for implementing MMMFA is developed. The experimental results on ORL and YALE face database show that the performance of MMMFA method is superior to those of PCA, LDA, LPP and MFA.