Abstract: The interpolation method based on seismic interference achieves the reconstruction of missing data successfully by using multiple waves, through the conversion of primary and multiple waves. However, the traditional interferometry suffers from severe wavelet deformation and the inability to reconstruct seismic data beyond the original maximum offset. In this paper, the third-order cumulant is introduced into the interference extrapolation method instead of the correlation calculation to extract the time delay. The calculation of the third-order cumulant does not include the calculation of autocorrelation, so the energy of the sidelobes is greatly weakened. The proposed method improves the resolution and signal-to-noise ratio of the reconstructed far-offset reflected wave by testing the horizontal layered geological model, deep-water salt model, fault model as well as the field data of ocean exploration. The high-order cumulant interference interpolation method can realize the high-quality extrapolation of the reflected wave, enhancing the energy of far-offset reflected wave. Moreover, the proposed method can improve the superposition times of far-offset data, and provide effective information for subsequent seismic processing.