Capsule networks can be considered to be the next era of deep learning and have recently shown their advantages in supervised classification. Instead of using scalar values to represent features, the capsule networks use vectors to represent features, which enriches the feature presentation capability. This paper introduces a deep capsule network for hyperspectral image (HSI) classification to improve the performance of the conventional convolutional neural networks (CNNs). Furthermore, a modification of the capsule network named Conv-Capsule is proposed. Instead of using full connections, local connections and shared transform matrices, which are the core ideas of CNNs, are used in the Conv-Capsule network architecture. In Conv-Capsule, the number of trainable parameters is reduced compared to the original capsule, which potentially mitigates the overfitting issue when the number of available training samples is limited. Specifically, we propose two schemes: (1) A 1D deep capsule network is designed for spectral classification, as a combination of principal component analysis, CNN, and the Conv-Capsule network, and (2) a 3D deep capsule network is designed for spectral-spatial classification, as a combination of extended multi-attribute profiles, CNN, and the Conv-Capsule network. The proposed classifiers are tested on three widely-used hyperspectral data sets. The obtained results reveal that the proposed models provide competitive results compared to the state-of-the-art methods, including kernel support vector machines, CNNs, and recurrent neural network.