On-board data compression is a critical task that has to be carried out with restricted computational resources for remote sensing applications. This paper proposes an improved algorithm for onboard lossless compression of hyperspectral images, which combines low encoding complexity and high-performance. This algorithm is based on hybrid prediction. In the proposed work, the decorrelation stage reinforces both intraband and interband predictions. The intraband prediction uses the median prediction model, since the median predictor is fast and efficient. The interband prediction uses hybrid context prediction which is the combination of a linear prediction (LP) and a context prediction. Eventually, the residual image of hybrid context prediction is coded by the Huffman coding. An efficient hardware implementation of both predictors is achieved using FPGA-based acceleration and power analysis has been done to estimate the power consumption. Performance of the proposed algorithm is compared with some of the standard algorithms for hyperspectral images such as 3D-CALIC, M-CALIC, LUT, LAIS-LUT, LUT-NN, DPCM (C-DPCM), JPEG-LS. Experimental results on AVIRIS data show that the proposed algorithm achieves high compression ratio with low complexity and computational cost.