The Quickly changed Doppler frequency offset is calculated and researched under low SNR during mobile satellite communications receiver carrier capture process. Firstly, current carrier frequency offset calculation technology is introduced, and the influence of the Doppler shift caused by the carrier capture is analyzed; Secondly, carrier frequency offset acquisition affected by changing rate of Doppler frequency offset is analyzed. Its mainly considered that first order changing rate and second order changing rate affect carrier acquisition. The changing rate would seriously reduces non-coherent accumulation number during carrier frequency offset estimation at low SNR; Finally, carrier frequency offset caused by the rate of change of the first order and second-order Doppler shift is analyzed and researched. It is demonstrated that platform effort caused by Doppler frequency offset can be improved, and the efficiency of the carrier capture increased through sampling points N reasonable by MATLAB simulation.