Precise object classification based on Hyperspectral imagery with limited training data presents a challenging task. We propose a tensor-based dictionary self-taught learning (TDSL) classification method to provide some insight into these challenges. The idea of TDSL is to utilize a small amount of unlabeled data to improve the supervised classification. The TDSL trains tensor feature extractors from unlabeled data, extracts joint spectral-spatial tensor features and performs classification on the labeled data set. These two data sets can be gathered over different scenes even by different sensors. Therefore, TDSL can complete cross-scene and cross-sensor classification tasks. For training tensor feature extractors on unlabeled data, we propose a sparse tensor-based dictionary learning algorithm for three-dimensional samples. In the algorithm, we initialize dictionaries using Tucker decomposition and update these dictionaries based on the K higher-order singular value decomposition. These dictionaries are feature extractors, which are used to extract sparse joint spectral-spatial tensor features on the labeled data set. To provide classification results, the support vector machine as the classifier is applied to the tensor features. The TDSL with the majority vote (TDSLMV) can reduce the misclassified pixels in homogenous regions and at the edges of different homogenous regions, which further refines the classification. The proposed methods are evaluated on Indian Pines, Pavia University, and Houston2013 datasets. The classification results show that TDSLMV achieves as high as $99.13\%$, $99.28\%$, and $99.76\%$ accuracies, respectively. Compared with several state-of-the-art methods, the classification accuracies of the proposed methods are improved by at least $2.5\%$.