In this paper, a novel discriminative dictionary learning with pairwise constraints by maximum correntropy criterion is proposed for pair matching problem. Comparing with the conventional dictionary learning approaches, the proposed method has several advantages: (i) It can deal with the outliers and noises problem more efficiently during the reconstruction step. (ii) It can be effectively solved by half-quadratic optimization algorithm, and in each iteration step, the complex optimization problem can be reduced to a general problem that can be efficiently solved by feature-sign search optimization. (iii) The proposed method is capable of analyzing non-Gaussian noise to reduce the influence of large outliers substantially, resulting in a robust and discriminative dictionary. We test the performance of the proposed method on two applications: face verification on the challenging restricted protocol of Labeled Faces in the Wild (LFW) benchmark and face-track identification on a dataset with more than 7,000 face-tracks. Compared with the recent state-of-the-art approaches, the outstanding performance of the proposed method validates its robustness and discriminability.