Single-image blind deconvolution is a challenging illposed inverse problem which requires regularization techniques to stabilize the restoration process. Its purpose is to recover an underlying blur kernel and a latent image from only one blurred image. In most imaging situations, the blur kernel is not only spatially sparse, but also piecewise smooth with the support of a continuous curve. Thus this paper proposes a hybrid regularized method to robustly estimate the blur kernel by incorporating both L1-norm of kernel intensity and squared L2-norm of intensity derivative. Once the blur kernel is estimated, a total generalized variation based image restoration model is developed to guarantee robust non-blind image deconvolution. All optimization problems related to blur kernel estimation and non-blind deconvolution in this paper will be efficiently solved using fast numerical algorithms. Numerous experiments have been conducted to compare our proposed method with some state-of-the-art blind deconvolution methods on both synthetic and real-world datasets. The experimental results have illustrated the effectiveness of our proposed method in terms of quantitative and qualitative image quality evaluations.