This paper proposes a new spatial regularization of Fisher linear discriminant analysis (LDA) to reduce the overfitting due to small size sample (SSS) problem in face recognition. Many regularized LDAs have been proposed to alleviate the overfitting by regularizing an estimate of the within-class scatter matrix. Spatial regularization methods have been suggested that make the discriminant vectors spatially smooth, leading to mitigation of the overfitting. As a generalized version of the spatially regularized LDA, the proposed regularized LDA utilizes the non-uniformity of spatial correlation structures in face images in adding a spatial smoothness constraint into an LDA framework. The region-dependent spatial regularization is advantageous for capturing the non-flat spatial correlation structure within face image as well as obtaining a spatially smooth projection of LDA. Experimental results on public face databases such as ORL and CMU PIE show that the proposed regularized LDA performs well especially when the number of training images per individual is quite small, compared with other regularized LDAs.