Since Mars is far away from Earth, the propagation delay between Mars and Earth is very large. To ensure the effective use of the link transmission bandwidth, China’s first Mars exploration mission has put forward a demand for data compression for all scientific payloads. The on-board mature algorithms for data compression are mainly focused on optical images and microwave imaging radar applications. No articles have been published on data compression methods that are applied to subsurface-penetrating radar. Based on the background of this application, this paper proposes a logarithmic lossy compression algorithm which can meet the mission requirements for high compression ratios of 4:1 and 2.5:1. Its compression error is less than that of the block adaptive quantization (BAQ) algorithm. The algorithm is not only easy to implement on field-programmable gate array (FPGA) platforms, but also offers simple ground decompression and fast imaging. The experimental results show that high compression ratios of 4:1 and 2.5:1 can be realized, even if the data in and between traces do not have a strong correlation. And its relative error is less than 2%, which is a new type of high-efficiency data compression method that can be implemented on-board to meet with the demand of subsurface penetrating radar.