Abstract: For secure release and privacy protection of color facial image, a recognition algorithm based on differential privacy in quaternion domain is introduced. Firstly, the pure quaternion matrix is selected to encode each color facial image as a whole. Then the differential privacy model is constructed by perturbing singular values with Laplacian noise through the exponential mechanism to ensure the discriminability of facial image data. Afterwards, a two-stage quaternion two-dimensional principal component analysis is utilized for learning filters. By combing hash encoding with block histogram, feature vectors are extracted and used for training support vector machine to complete facial image recognition. The experimental results on three publicly multimodal facial datasets demonstrate that the accuracy of the proposed algorithm is significantly promoted in comparison with those by using the existed three algorithms, where the maximum accuracy is up to 95% in facial recognition task. It not only effectively protects the privacy information in facial images, but also achieves high recognition accuracy, which has security and availability.