Aiming at the problem of motion image deblurring, a fuzzy kernel method based on L0 norms regularization term is presented. This method applies the image gradient L0 norms as the regularization term to construct a non-convex optimization energy function through the sparse prior condition of the image and the appropriate parameter estimation method. In the process of solving the function, the alternating iteration method is used to update the original image and the estimated values of the fuzzy kernel. In the process of original image estimation, the sparse regularization term of the image gradient L0 norms can effectively retain the sharp edges as well as suppress the influence of the weak edges on the fuzzy kernel estimation, which can obviously improve the accuracy of kernel estimation. In the process of fuzzy kernel calculation, the optimization energy function of fuzzy kernel converts to a classic convex optimization. Using the fast Fourier transform to compute the energy function can quickly get the estimated kernel. After getting the appropriate kernel of image, the problem of image blind deconvolution can be converted to the image non-blind deconvolution. A hyper-Laplacian priors using L0.5 as the regularization term is applied in deconvolution. This algorithm can well model the heavey-tailed distribution of gradients in natural scenes so that a perfect result can be obtained. Experimental results demonstrate that the proposed method gets higher quality deblurring results than the previous methods.