In order to avoid beam splitter(BS)eavesdropping problem during quantum key distribution between a ground station and a satellite in a low earth orbit，the single-photon sources with Poisson distribution areanalyzed， the theoretical model of quantum bit rate is established and the expression of eavesdropping ratio in BSeavesdropping is given. The BS eavesdropping is analyzed for quantum key distribution between a ground stationand a satellite in a low earth orbit. The results show that mean photon number per pulse can be optimized and thateavesdropping ratio is on the order of 10一a，and by error detection and privacy amplification，the information gainedby an eavesdropper can be reduced to less than 1 bit. This means that it is feasible to implement quantum key dis-tribution between a ground station and a satellite in a low earth orbit. Security can be guaranteed in a high quantumbit exchanging rate system.