To reduce feature dimensions while obtaining robust classifi- cation, in this paper, we propose quaternion sparse discriminant analysis (QSDA) for color face recognition. QSDA is formulated as a quaternion sparse regression-type model. It employs the quaternion algebra to provide an elegant and holistic way to represent color face images. The succeeding operations are directly applied to two-dimensional quaternion matrices, and hence QSDA is computationally efficient and well preserves the spatial structure of color face images. Benefited from sparsity constraints, QSDA is robust for classification. An alternating minimization algorithm is designed to solve QSDA. Experimental results demonstrate the effectiveness of QSDA for color face recognition, especially for partially occluded color face images