Effective lossy algorithms for compressing hyperspectral images using singular value decomposition (SVD) and discrete cosine transform (DCT) have been presented in this paper. A Hyperspectral image consists of a number of bands and each band contains some specific information. This paper suggests two compression algorithms that are used to compress the hyperspectral images by considering hyperspectral image data, band-by-band and applying compression to each band employing SVD and DCT. The compression performance of the resultant images are evaluated using various objective image quality metrics and are found to be attractive for hyperspectral image compression.