Most of the existing statistical a priori image blind deblurring methods have limited edge and detail recovery ability. To solve this problem, we proposed a new blind deblurring algorithm. First, by using the downsampling, the multi-scale decomposition of an image was performed based on pyramid decomposition. Then, in each image layer, the significant intensity a priori was used to extract the image edge, and the low gradient rank a priori was employed to suppress the blurring effect and noise. Next, the coarse-to-fine strategy was used to alternatively iterate the blur kernel and latent image to obtain an accurate final blur kernel. Finally, a clear image was recovered by a non-blind deconvolution method. Further, to reduce the iteration time of the multi-scale iteration, an adaptive iterative strategy was proposed. In this strategy, the number of iterations was adjusted by the similarity evaluation of the estimated blur kernels, and the computational cost was effectively reduced. The experimental results show that the proposed algorithm can accurately estimate the blur kernel and effectively suppress the influence of noise; also, the recovered image contains more edge and detail information.