In this paper, a Doppler scaling fast Fourier transform (Doppler-FFT) algorithm for filter bank multi-carrier (FBMC) is proposed, which can efficiently eliminate the impact of the Doppler scaling in satellite communications. By introducing a Doppler scaling factor into the butterfly structure of the fast Fourier transform (FFT) algorithm, the proposed algorithm eliminates the differences between the Doppler shifts of the received subcarriers, and maintains the same order of computational complexity compared to that of the traditional FFT. In the process of using the new method, the Doppler scaling should be estimated by calculating the orbital data in advance. Thus, the inter-symbol interference (ISI) and the inter-carrier interference (ICI) can be completely eliminated, and the signal to interference and noise ratio (SINR) will not be affected. Simulation results also show that the proposed algorithm can achieve a 0.4 dB performance gain compared to the frequency domain equalization (FDE) algorithm in satellite communications.