Abstract: Aiming to solve the problem of large calculation amount of generating point spread function (PSF) dictionary by grating lobes and broadband Richardson-Lucy (R-L) deconvolution of sparse line arrays, a broadband wavenumber domain R-L deconvolution method for sidelobe suppression in beamforming is proposed. The method takes advantages of the characteristics of the broadband beamforming technology in the frequency-wavenumber domain with constant beam width, which allows all frequency points to share one PSF dictionary for deconvolution computation to reduce the storage space and computational complexity of the PSF for deconvolution. Combined with the periodic shift relationship between sidelobes and the main lobe in the frequency-wavenumber domain beamforming algorithm, good suppression performance can be achieved by utilizing practical beamforming main lobe azimuth, width and energy to predict and suppress aliasing artifacts based on actual data. The performance of the proposed method was verified through simulation and experimental data. Compared with conventional broadband deconvolution processing, the results show that the method can reduce the amount of calculation and the grating lobe suppression effect is greater than 6 dB, expanding the detection and resolution performance of the array for broadband targets under the same number of array elements.