The huge amount of convex grating imaging spectrometer image data brings much pressure to data transmission and storage, so the image must be compressed in real time. Firstly, the image characteristics were analyzed according to the imaging principle, and the compression approach to removing spatial correlation and spectral correlation was achieved; Secondly, the compression algorithms were analyzed and the 3-D compression scheme of one-order linear compression in spectral dimension and JPEG2000 compression in spatial dimension was proposed. Finally, a real-time compression system based on FPGA and ADV212 was designed, in which FPGA was used for logic control and implementation of prediction algorithm, and ADV212 was used for JPEG2000 compression. The analysis result shows that the system has the ability of lossless and lossy compression, enabling real-time image compression.