In order to study the influence of rainfall on the transmission quality and quantum communication performance of the satellite-to-ground quantum links, this paper analyzes the relationship between rainfall intensity, extinction coefficient of raindrops and attenuation coefficient of the satellite-to-ground links based on the M-P raindrop spectra and the Mie scattering theory, establishes the model of relationship between the capacity and average fidelity of information channels under the rainfall background, and obtains the teleportation fidelity under rainfall environment on the basis of the two-particle entangled state probabilistic teleportation scheme. The theoretical analysis and simulation results show that the increase of rainfall intensity results in the increase of extinction coefficient, which further leads to the decrease of capacity and average fidelity of information channels. At the same time, rainfall causes the channel entanglement degree to be weakened, thereby reducing the fidelity of teleportation. Therefore, rainfall has a significant impact on the performance of the quantum satellite-to-ground links, and the various parameters in the satellite-to-ground quantum links must be appropriately adjusted according to rainfall intensity in order to ensure the communication quality.