The efficient onboard lossless compression is very important for the real-time transmission of hyperspectral images. Due to the shortages of the traditional joint encoding and decoding algorithms of hyperspectral images, a lossless compression algorithm based on distributed source coding （DSC） was proposed. To make use of the local spatial correlation, multiple linear regression was employed to construct the side information of each block, and the optimal predictive order was determined for each block in order to make full use of the local spectral correlation. According to the principle of (n, k) linear grouping codes, distributed lossless coding of hyperspectral images was realized by using multilevel coset codes. Experimental results show that the proposed algorithm achieved competitive compression performance and low complexity compared with those existing classical algorithms, which is suitable for the onboard compression of hyperspectral images.