We present an effective blind image deblurring method based on the reweighted L₁ norm prior. The prior is motivated by that the traditional L₁ norm highly depends on the pixel itself, that is, the larger the pixel value, the greater the penalty. However, the blur reduces the high-frequency components of the clear image, and minimizing the high-frequency part will result in a blur solution or delta function kernel. To overcome this limitation, we employ the reweighted L₁ norm and it eliminates this dependence within wisely weighting. The image prior compensates for the degeneration of high intensities and greatly stabilizes the intermediate image estimation process. However, the prior proposed introduces a challenging optimization problem. We develop an efficient optimization scheme to obtain a reliable intermediate image for estimating the blur kernel. Extensive experiments on different kinds of challenging blurry images demonstrate the superiority of our proposed method over the state-of-the-art blind deblurring methods. Moreover, our blind deblurring algorithm is effective in various scenarios, such as natural, text, and low-light images.