This paper investigates an accurate frequency offset estimator in the intermediate frequency for the satellite-based AIS signals. Using Gaussian Minimum Shift Keying (GMSK) modulation for transmission, the AIS signal is shown to be a plane wave with the modulated phase information and carrier frequency resulting from the Doppler effects. Hence, the phase information can be eliminated with a re-modulated signal, and the frequency offset can be estimated by the ratio of the maximum spectral amplitude and its neighbor spectral amplitude based on the FFT interpolation. The estimator has low complexity, and it is easy to implement. Computer simulations are used to assess the estimation performance of the estimator.