A stable explicit depth wavefield extrapolation is obtained using iterative reweighted least-squares (IRLS) frequency-space (-) finite-impulse response digital filters. The problem of designing such filters to obtain stable images of challenging seismic data is formulated as an IRLS minimization. Prestack depth imaging of the challenging Marmousi model data set was then performed using the explicit depth wavefield extrapolation with the proposed IRLS-based algorithm. Considering the extrapolation filter design accuracy, the IRLS minimization method resulted in an image with higher quality when compared with the weighted least-squares method. The method can, therefore, be used to design high-accuracy extrapolation filters.