Most hyperspectral image (HSI) data exist in the form of tensor; the tensor representation preserves the potential spatial-spectral structure information compared with the vector representation, which can help improve the classification performance of HSI. In this article, a deep high-order tensor convolutional sparse coding (CSC) model is proposed, which can be used to train deep high-order filters. Based on the deep high-order tensor CSC model, a deep feature extraction network (DHTCSCNet) is constructed, which is used for feature extraction of HSIs. By combining the spectral-spatial feature and the features extracted by the proposed DHTCSCNet at each layer, a combined feature that incorporates shallow, deep, spectral, and spatial features can be obtained. Then, the graph-based learning (GSL) methods are used to classify the combined feature. Experimental results show that the DHTCSCNet can obtain better classification performance compared with other HSI classification methods.