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In order to improve the phase jitter caused by dynamic stress error and thermal noise in satellite communication system, the demodulation loss of the signal is obvious when tracking the carrier wave of the large dynamic signal at low SNR, in this paper, a carrier tracking algorithm based on Dopler rate of change estimation is proposed. First, the Dopler rate of change and Dopler frequency of the received signal are estimated by the method of delay-correlated Fast Fourier Transformation（FFT） and FFT analysis, then the Doppler rate of change and the frequency of the received signal are compensated by the estimated value, and finally the compensated signal is tracked by the third-order PLL, and the symbol rate is considered, the algorithm is improved and simulated. The simulation results show that this method can achieve stable carrier tracking with a symbol rate of 1 Mbps and a tracking rate of 150 kHz/s at a carrier-to-noise ratio of 63 dBHz, and the demodulation loss is less than 0.3 dB. By using this algorithm, the carrier tracking complexity can be reduced and the tracking precision can be improved, which provides a basis for the improvement of the carrier tracking module of the receiver.