In the signal demodulation process of the satellite coherent optical communication system, the relative motion of the satellite will cause the received signal light to produce a Doppler frequency shift of GHz magnitude. The long-distance transmission of the signal light leads to an extremely low optical signal-to-noise ratio. The traditional method cannot compensate for the large-scale Doppler frequency shift at a low signal-to-noise ratio, which seriously affects the ability of the communication system. In view of the above problems, this paper proposes a two-stage frequency acquisition algorithm, which includes two stages: automatic frequency sweeping and frequency locking control. In the automatic frequency scanning stage, the frequency difference is reduced to the order of 100 MHz by the local oscillator's automatic frequency scanning. In the frequency locking control stage, the frequency difference is further reduced to the MHz level at a low signal-to-noise ratio through high-precision local oscillator frequency control and FFT transformation. The simulation results show that the algorithm can compensate for the Doppler frequency difference in the 10 GHz range of the large dynamic range under the 2 dB signal-to-noise ratio, and meet the demodulation requirements of the satellite cohe-rent optical communication.