The Doppler effect severely degrades the orthogonality of orthogonal frequency division multiplexing (OFDM) systems, and is a severe problem in the underwater acoustic (UWA) communications, leading to nonuniform Doppler shifts for all subcarriers. In order to alleviate Doppler effect, resampling technique by oversized fast Fourier transform (FFT) can achieve fast and accurate resampling in frequency domain. Nevertheless, the accuracy of this conventional FFT based approach depends on the FFT size, which in turn increases receiver complexity. In order to overcome this problem, the Doppler compensation model in frequency domain is simplified by Taylor series expansion in this letter. Based on the simplified model, we propose the Doppler compensation algorithm by using FFT and interpolation to achieve higher compensation accuracy. Simulation results demonstrate that the proposed algorithm shows very similar bit error rate (BER) performance with that of Chirp Z-transform (CZT) based method. However, the complexity of our proposed algorithm is about half of CZT based method. Further, our proposed low-complexity Doppler compensation algorithm can also be applied to the sampling frequency offset (SFO) correction in terrestrial OFDM communication systems.