Abstract: Considering the difficulty of obtaining orthogonal eigenvector set of quaternion matrix, a novel obtaining method is proposed in this paper. The main idea of this method can be described as follows. Firstly, construct the educing matrix of quaternion matrix, which is defined in complex field, secondly get complex eigenvector by using a specific space, which is similar to the eigenvector space of the educing matrix, then the orthogonal eigenvector set can be obtained through transforming the eigenvectors of all eigenvalues to quaternion eigenvectors. Simultaneously, quaternion-based principal component algorithm (PCA) method is proposed and detailed mathematical calculations are also given to explain its rationality and practicability in pattern recognition field. Finally, quaternion-based color face recognition method, which uses R, G, B as the three imaginary numbers of quaternion, is proposed in the paper. Compared with the traditional method, our algorithm uses face grayscale information and color information at the same time in order to get more discrimination information. Experiments performed on color face database of TianSi brainpower graduate school of Sichuan University indicate that the recognition rates are improved significantly and the proposed method is superior to the traditional one in the mass.