Single-image blind deblurring is a challenging ill-posed in- verse problem which aims to estimate both blur kernel and latent sharp image from only one observation. This paper fo- cuses on first estimating the blur kernel alone and then restor- ing the latent image since it has been proven to be more feasi- ble to handle the ill-posed nature during blind deblurring. To estimate an accurate blur kernel, L0-norm of both first- and second-order image gradients is proposed to regularize the final estimation result. The proposed L0-regularized hybrid gradient sparsity priors obtain major benefit from the intrin- sic sparsity properties of images and can assist in guarantee- ing high-quality blur kernel estimation. Once the blur kernel is estimated, the final clean image is robustly generated using the combination of L1-norm data-fidelity term and total vari- ation regularizer. Experimental results have demonstrated the satisfactory performance of the proposed method.