Edge-preserving image smoothing is a key preprocessing step of many computer vision and graphics algorithms. Edge-preserving image smoothing algorithm based on l1 norm outperforms many existing image smoothing algorithms. However, there are still many remaining textures in the smoothed results. In order to improve the smoothing effect of the algorithm, a new image smoothing algorithm based on reweighted l1 norm was proposed. The proposed algorithm combines the original l1 norm-based image smoothing algorithm and reweighed l1 norm minimization. The solution was made sparser through the reweighting method. The performance of the algorithm was evaluated through experiments. Experimental results show that, compared to the original l1 norm-based image smoothing algorithm and several other existing image smoothing algorithms, the proposed algorithm can smooth images very effectively and there is little texture remained in the smoothed results. Using reweighted l1 norm can improve the smoothing effect of the original l1 norm-based image smoothing algorithm.