Hyperspectral imagers are developing towards high resolution, high detection sensitivity, broad spectra, and wide coverage, which means that hyperspectral data are getting more and more substantial. This brings a great challenge to data storage and real-time transmission of hyperspectral data. A compression method based on Tucker decomposition and CANDECOMP/PARAFAC decomposition (TD-CP) is proposed. The hyperspectral data are treated as a third-order tensor. First, TD is performed on the hyperspectral data to obtain a core tensor and three factor matrices, and then CP decomposition is performed on the core tensor. Compared with principal component analysis (PCA) + JPEG2000, TD, and CP, TD-CP can retain spatial information and spectral information better at the same time, and running time is shorter.