Infrared hyperspectral imaging is an important technical means to obtain the emissivity spectra and temperature of land surface target, and is an important development direction of spaceborne optical remote sensing in the future. Under the natural rugged land surface condition, the quality of infrared hyperspectral imaging data is affected by terrain condition, atmospheric condition and instrument performance. Therefore, the instrument signal-to-noise ratio and the calibration accuracy could not directly describe the measurement accuracy of the hyperspectral characteristics of target. An uncertainty prediction model of spaceborne infrared hyperspectral images over rugged land surface is established, in this paper. This model could simulate the surface scene, the atmospheric radiation transfer over rugged land surface, and the imaging process of the spaceborne spectrometer. At the same time, the uncertainty transfer from the surface signal to the restored radiance data product could be realized. The generated uncertainty results include the fluctuation of the surface signal, the error of the atmospheric transmission model, the influence of topographic relief, the response characteristics of the imaging spectrometer and the calibration uncertainty. Based on this model, we can also realize the ranking of the uncertainty contribution of the above links, which could help to identify the weak link in the remote sensing measurement chain. The random simulation experiments over a rugged desert scene were conducted to verified the model. It is indicated that more than 99.9% of the stochastic simulation radiance spectra are in the range of the predicted uncertainty.