High-resolution deconvolution can mathematically be viewed as a regularized inverse problem. Besides, the result of the high-resolution deconvolution is generally accepted as reflectivity series of the layered media. On the other hand, lateral continuity is frequently poorer than vertical resolution on post-stack seismic section after application of any high-resolution deconvolution. However, because of the ill-posed inherent of the deconvolution problem, the Cauchy norm regularization term, a non-quadratic prior-information is widely used to provide the stability and uniqueness of the problem. But, it does not provide adequate quality of deconvolution if the noise in the data is strong. In this study, a stable and high-resolution deconvolution of post-stack seismic data was accomplished by an iterative inversion algorithm incorporating the Cauchy norm regularization with FX filter weighting. Cauchy norm regularization was utilized to force the solution to a spikiness structure, while the effective random noise reduction was performed by using the FX filter. Applications to synthetic and real post-stack data showed that the resolution in the vertical direction and continuity in the lateral direction are better improved. Thus, we think that this process makes seismic sections obtained especially from thin layered sedimentary basins more interpretable.