A new algorithm for removing the Gibbs-like artifacts in image denoising is presented. The original image is decomposed by using the nonsubsampled pyramid filter (NSPF) and the decomposed image model is built based on total variation model. Then the preliminary denoised image is produced by reconstruction. A detail compensation image is further obtained by using the difference between the preliminary denoised image and the original image. Finally,the denoised image can be obtained by adding the compensation image to the reconstructed image. Experiments show that the proposed scheme can remove Gibbs-like artifacts and image noise effectively. This algorithm outperforms the existing schemes in regard of both the peak-signal-to-noise-ratio (PSNR) and the edge preservation ability.