To solve the problem that hyperspectral image data has many dimensions and it is difficult to extract spectral information and spatial information, a classification algorithm is proposed based on a hypergraph and a convolutional neural network. In this algorithm, the hypergraph is first constructed based on the spectral and spatial relationships among pixels in a hyperspectral image, and then a sample with spectral space joint features is constructed through this hypergraph, which is finally sent to the convolutional neural network for feature extraction and thus the classification is finally achieved. The experiment is performed on three most commonly used hyperspectral datasets and an overall classification accuracy of 96.63% on the Indian Pines dataset is achieved. Compared with other algorithms, the proposed algorithm has a high classification accuracy and a high speed, which avoids the instability in feature extraction and fusion by traditional methods. It is verified that the spectral space joint information extracted by the proposed algorithm has a strong feature expression of hyperspectral images.