Learning an expressive representation from multi-view data is a key step in various real-world applications. In this paper, we propose a semi-supervised multi-view deep discriminant representation learning (SMDDRL) approach. Unlike existing joint or alignment multi-view representation learning methods that cannot simultaneously utilize the consensus and complementary properties of multi-view data to learn inter-view shared and intra-view specific representations, SMDDRL comprehensively exploits the consensus and complementary properties as well as learns both shared and specific representations by employing the shared and specific representation learning network. Unlike existing shared and specific multi-view representation learning methods that ignore the redundancy problem in representation learning, SMDDRL incorporates the orthogonality and adversarial similarity constraints to reduce the redundancy of learned representations. Moreover, to exploit the information contained in unlabeled data, we design a semi-supervised learning framework by combining deep metric learning and density clustering. Experimental results on three typical multi-view learning tasks, i.e., webpage classification, image classification, and document classification demonstrate the effectiveness of the proposed approach.