Blind motion deblurring is an important problem that receives enduring attention in last decade. Based on the observation that a good intermediate estimate of latent image for estimating motion-blur kernel is not necessarily the one closest to latent image, edge selection has proven itself a very powerful technique for achieving state-of-the-art performance in blind deblurring. This paper presented an interpretation of edge selection/reweighting in terms of variational Bayes inference, and therefore developed a novel variational expectation maximization (VEM) algorithm with built-in adaptive edge selection for blind deblurring. Together with a restart strategy for avoiding undesired local convergence, the proposed VEM method not only has a solid mathematical foundation but also noticeably outperformed the state-of-the-art methods on benchmark datasets.