Abstract: The infrared imaging grayscale variation caused by the influence of atmosphere on infrared radiation transmission is a problem that infrared target tracking application needs to cope with. The law of infrared imaging grayscale variation in Lie group was modeled, which was important to design an efficient and robust target tracking algorithm. Firstly the infrared radiation transmission model was analyzed, and then the brightness model of infrared imaging was derived by considering the mechanism of infrared imaging. Furthermore, it was theoretically proved that the infrared imaging grayscale variation caused by the atmosphere obeyed the Lie group structure, and a non-Euclidean mathematical representation of the infrared imaging grayscale variation was proposed. Finally, according to the infrared imaging grayscale variation model, the field experimental data collected under different environments were fitted. The regression analysis results demonstrate the correctness of the model, which validates the rationality of the Lie group representation of the infrared imaging grayscale variation.