Abstract: The expressions of single-photon acquisition probability in free-space quantum key distribution were deduced based on TEM10 mode Laguerre-Gaussian beams. The single-photon acquisition was analyzed for the laser link between a ground station and a satellite in a low earth orbit. The results show that single-photon can be acquired by the receiver in the satellite with maximum probability if highly attenuated laser pulses based on TEM10 mode Laguerre-Gaussian beams are used as single-photon sources and a bright precursor reference pulse is used to set a short time window for the single-photon acquisition. Unlike the fundamental-mode Gaussian beam, the TEM10 mode Laguerre-Gaussian beam does not cause the single-photon acquisition probability losses due to the movement of satellites.