Single-image blind deblurring is a challenging ill-posed inverse problem which aims to estimate both blur kernel and latent sharp image from only one observation. This paper focuses on first estimating the blur kernel alone and then restoring the latent image since it has been proven to be more feasible 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 intrinsic sparsity properties of images and can assist in guaranteeing 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 variation regularizer. Experimental results have demonstrated the satisfactory performance of the proposed method.