Hyperspectral remote sensing technology is widely used in marine remote sensing, geological exploration, atmospheric and environmental remote sensing. Owing to the rapid development of hyperspectral remote sensing technology, resolution of hyperspectral image has got a huge boost. Thus data size of hyperspectral image is becoming larger. In order to reduce their saving and transmission cost, lossless compression for hyperspectral image has become an important research topic. In recent years, large numbers of algorithms have been proposed to reduce the redundancy between different spectra. Among of them, the most classical and expansible algorithm is the Clustered Differential Pulse Code Modulation (CDPCM) algorithm. This algorithm contains three parts: first clusters all spectral lines, then trains linear predictors for each band. Secondly, use these predictors to predict pixels, and get the residual image by subtraction between original image and predicted image. Finally, encode the residual image. However, the process of calculating predictors is timecosting. In order to improve the processing speed, we propose a parallel C-DPCM based on CUDA (Compute Unified Device Architecture) with GPU. Recently, general-purpose computing based on GPUs has been greatly developed. The capacity of GPU improves rapidly by increasing the number of processing units and storage control units. CUDA is a parallel computing platform and programming model created by NVIDIA. It gives developers direct access to the virtual instruction set and memory of the parallel computational elements in GPUs. Our core idea is to achieve the calculation of predictors in parallel. By respectively adopting global memory, shared memory and register memory, we finally get a decent speedup.