The amount of data generated by ultraspectral sounders is so large that considerable savings in data storage and transmission bandwidth can be achieved using data compression. Due to this large amount of data, the data compression time is of utmost importance. Increasing the programmability of the commodity Graphics Processing Units (GPUs) offer potential for considerable increases in computation speeds in applications that are data parallel. In our experiments, we implemented a spectral image data compression method called Linear Prediction with Constant Coefficients (LP-CC) using NVIDIA's CUDA parallel computing architecture. LP-CC compression method represents a current state-of-the-art technique in lossless compression of ultraspectral sounder data. The method showed an average compression ratio of 3.39 when applied to publicly available NASA AIRS data. We achieved a speed-up of 86 compared to a single threaded CPU version. Thus, the commodity GPU was able to significantly decrease the computational time of a compression algorithm based on a constant coefficient linear prediction.