Global secure communication networks could become ture by use of quantum cryptography and satellite. However, satellite-to-ground quantum key distribution (QKD) systems by using of commercial single photon counting module (SPCM) are facing a challenge of spatial-light-to-multimode-fiber coupling on the receiver end. Spatial light-to-multimode-fiber coupling qualification puts strict restricts on pointing and tracking precision of satellite-to-ground QKD systems. It is indicated by theoretical analysis and quantificational calculation that QKD systems work normally with a high photon detection probability when the ratio of tracking error ε to beam divergence θdiv is below 0.5, and that QKD systems could work better when ε/θdiv≤0.1 with a quantum key rate of a few kb/s. Light with shorter wavelength is more favorable to spatial-light-to-multimode-fiber coupling, and to achieve a higher quantum key production rate as well.