Image set based classification (ISC) has attracted lots of research interest in recent years. Several ISC methods have been developed, and dictionary learning technique based methods obtain state-of-the-art performance. However, existing ISC methods usually transform the image sample of a set into a vector for subsequent processing, which breaks the inherent spatial structure of image sample and the set. In this paper, we utilize tensor to model an image set with two spatial modes and one set mode, which can fully explore the intrinsic structure of image set. We propose a novel ISC approach, named discriminant tensor dictionary learning with neighbor uncorrelation (DTDLNU), which jointly learns two spatial dictionaries and one set dictionary. The spatial and set dictionaries are composed by set-specific sub-dictionaries corresponding to the class labels, such that the reconstruction error is discriminative. To obtain dictionaries with favorable discriminative power, DTDLNU designs a neighbor-uncorrelated discriminant tensor dictionary term, which minimizes the within-class scatter of the training sets in the projected tensor space and reduces tensor dictionary correlation among set-specific sub-dictionaries corresponding to neighbor sets from different classes. Experiments on three challenging datasets demonstrate the effectiveness of DTDLNU.