For the scientific exploration and research on Mars, it is an indispensable step to transmit high-quality Martian images from distant Mars to Earth. Image compression is the key technique given the extremely limited Mars-Earth bandwidth. Recently, deep learning has demonstrated remarkable performance in natural image compression, which provides a possibility for efficient Martian image compression. However, deep learning usually requires large training data. In this paper, we establish the first large-scale high-resolution Martian image compression (MIC) dataset. Through analyzing this dataset, we observe an important non-local self-similarity prior for Marian images. Benefiting from this prior, we propose a deep Martian image compression network with the non-local block to explore both local and non-local dependencies among Martian image patches. Experimental results verify the effectiveness of the proposed network in Martian image compression, which outperforms both the deep learning based compression methods and HEVC codec.