Image motion deblurring with unknown blur kernel is an ill-posed problem. This paper proposes a blind motion deblurring approach that solves blur kernel and the latent image robustly. For kernel optimization, an edge mask is used as an image prior to improve kernel update, then an edge selection mask is adopted to improve image update. In addition, an alternative iterative method is introduced to perform kernel optimization under a multiscale scheme. Moreover, for image restoration, a total-variation-(TV-) based algorithm is proposed to recover the latent image via nonblind deconvolution. Experimental results demonstrate that our method obtains accurate blur kernel and achieves better deblurring results than previous works.