Unmanned Aerial Vehicles (UAVs) are critical to the military and have enormous potential for expansion, but they are vulnerable to jamming on the battlefield, reducing the quality of communication links and operational effectiveness. Low-Earth orbit (LEO) satellites can be used as auxiliary communication nodes to enhance the communication stability of UAV networks in a complex electromagnetic environment. Therefore, in this paper, we establish a model of a LEO satellite-assisted UAV network in a spectrum denial environment. We propose a routing optimization algorithm based on simulated annealing to improve communication quality through route planning and a reasonable allocation of network bandwidth resources. Numerical results verify the efficiency of the proposed algorithm, and the advantages of LEO satellite-assisted UAV networks in terms of data transmission are also analyzed.