Linear Discriminant Analysis (LDA) is a well-known feature extraction method for supervised subspace learning in statistical pattern recognition. In this paper, a novel method of LDA based on a new L1-norm optimization technique and its variances are proposed. The conventional LDA, which is based on L2-norm, is sensitivity to the presence of outliers, since it used the L2-norm to measure the between-class and within-class distances. In addition, the conventional LDA often suffers from the so-called small sample size (3S) problem since the number of samples is always smaller than the dimension of the feature space in many applications, such as face recognition. Based on L1-norm, the proposed methods have several advantages, first they are robust to outliers because they utilize the L1-norm, which is less sensitive to outliers. Second, they have no 3S problem. Third, they are invariant to rotations as well. The proposed methods are capable of reducing the influence of outliers substantially, resulting in a robust classification. Performance assessment in face application shows that the proposed approaches are more effectiveness to address outliers issue than traditional ones.