Abstract: A joint estimation method of Doppler frequency shift and Doppler frequency rate based on interpolation is proposed for achieving fast carrier synchronization of burst in mobile satellite communication system under the circumstance of low Signal-to-Noise Ratio (SNR). In the proposed method, a coarse estimation of Doppler frequency shift and Doppler frequency rate is achieved first by a Doppler frequency rate searching combined with a traditional low-complexity frequency-estimating algorithm. The log-likelihood function of three Doppler frequency rate testing values, with the coarse estimation result as the center, is calculated and then an interpolation is taken to decide the final estimation of Doppler frequency rate. Finally, the frequency-estimating algorithm is used again to get the final estimation of Doppler frequency shift. Simulation results show that the proposed method has a low SNR threshold and an estimation performance close to Cramer-Rao Low Bound (CRLB). And it has a complexity by far the less than the max-likelihood algorithm and so is very applicable.