Abstract: The reconstruction of seismic signals is of great significance,and the Fourier reconstruction algorithm has re- ceived extensive attention. These algorithms have some advantages of simple principle,pure data drive and little as- sumption. However,there are also the shortcoming of slow computation speed. Therefore,on the basis of FRMN,the new algorithm of Fourier Reconstruction with accelerated Landweber Iteration (FRLI) was put forward. Based on the classical FRMN,the algorithm uses accelerated Landweber iteration to solve the Fourier coefficients. Then the seismic signals were reconstructed through the inverse Fourier transform. Through the reconstruction experiments of seismic sig- nals with different dimensions,the results show that the FRLI greatly improves the reconstruction speed and the recon- struction effect is better than the classic FRMN and FRSI reconstruction algorithms. Therefore,the FRLI algorithm for reconstructing seismic signals can solve the defects of traditional algorithms.