Image smoothing is a fundamental part of many computer vision and graphics tasks. In this paper, to improve the sparsity of the gradient norm of the smoothing image, we use nonconvex penalty functions as regularization terms. A condition on nonconvex regularizers is given to ensure that the objective functions are strictly convex. We apply the powerful majorization-minimization algorithm for solving the convex image smoothing models. Proof of global convergence for the MM algorithm is provided. The superiority of the proposed method in terms of PSNR, SSIM and visual quality is verified through comprehensive experiments in a variety of applications.