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Recently, the hyperspectral image (HSI) classification methods based on convolutional neural networks (CNN) have developed rapidly with the advance of deep learning (DL) techniques. In order to more efficiently extract spatial and spectral features, we propose an end-to-end cubic CNN (Cubic-CNN) in this article. The proposed Cubic-CNN is a supervised DL framework that significantly improves classification accuracy and shortens training time. Specifically, Cubic-CNN employs the dimension reduction method combined with principal component analysis and 1-D convolution to remove redundant information from HSIs. Then, convolutions are performed on the planes in different directions of the feature cube data to fully extract spatial and spatial-spectral features and fuse the features from different dimensions. In addition, we performed batch normalization on the data cube after each convolutional layer to improve the performance of the network. Extensive experiments and analysis on standard datasets show that the proposed algorithm can outperform the existing state-of-the-art DL-based methods.