The wavelet transform is widely used in the task of hyperspectral image compression (HSIC). They have achieved outstanding performance in the compression of a hyperspectral (HS) image, which has attracted great interest. However, transform based hyperspectral image compression algorithm (HSICA) has low-coding gain than the other state of art HSIC algorithms. To solve this problem, this manuscript proposes a curvelet transform based HSIC algorithm. The curvelet transform is a multiscale mathematical transform that represents the curve and edges of the HS image more efficiently than the wavelet transform. The experiment results show that the proposed compression algorithm has high-coding gain, low-coding complexity, at par coding memory requirement, and works for both (lossy and lossless) compression. Thus, it is a suitable contender for the compression process in the HS image sensors.