A novel approach to learn a discriminative dictionary over a tensor sparse model is presented. A structural incoherence constraint between dictionary atoms from different classes is introduced to promote discriminating information into the dictionary. The incoherence term encourages dictionary atoms to be as independent as possible. In addition, we incorporate classification error into the objective function of dictionary learning. The dictionary is learned in a supervised setting to make it useful for classification. A linear multi-class classifier and the dictionary are learned simultaneously during the training phase. Our approach is evaluated on three types of public databases, including texture, digit, and face databases. Experimental results demonstrate the effectiveness of our approach.