Abstract: To ease the singularity of within-class scatter matrix due to the small sample size problem for linear discriminant analysis (LDA) method,the modified 2D linear discriminant analysis and bi-directional linear discriminant analysis method based on quaternion matrix were proposed to recognize a color face.These methods made full use of the information of the spatial distribution of color images,and extracted the 2DLDA or BDLDA feature by reducing the dimensionality in both column and row directions,and smoothed the singularity of the within-class scatter matrix.By using the FERET color face database and AR color face database,experimental results show that this approach has better recognition performance than the 2DPCA or BDPCA method based on quaternion matrix.