The existing hyperspectral image compression algorithms that aim at high compression quality generally have problems such as high computational complexity, off-line processing, and difficulty in implementing an embedded platform. They are difficult to be implemented in practical applications at present. To resolve the above problems, a real-time compression method for embedded hyperspectral images based on Karhunen-Loeve Transform (KLT) and HEVC (High Efficiency Video Coding) was designed. Firstly, the inter-spectral correlation was reduced by KLT. Then, the spatial correlation was removed by HEVC. Finally, the process of quantization and entropy coding was accomplished by HEVC. Based on NVIDIA Jetson TX1 platform, a heterogeneous parallel compression system which utilizes both the CPU and GPU was designed and implemented. Using real data sets, the performance of the designed algorithm and the practicability of the implemented platform were verified. The experimental results show that compared with the Discrete Wavelet Transform (DWT)+JPEG2000 algorithm, the reconstruction accuracy is improved significantly under the same compression ratio. The Peak Signal-to-Noise Ratio (PSNR) is increased by 1.36 dB on average; at the same time, compared with CPU, performing KLT calculations on GPU can also reduce the runtime by 33% at most.