This paper proposes a new method for natural-image deblur based on a single blurred image. The natural image prior, a sparse gradient distribution, is enforced using a gradient histogram remapping method in the proposed deblur algorithm. The proposed objective function for blind deconvolution is solved by an alternating minimization method. The point spread function and the unblurred image are updated alternately. The proposed method is able to produce high-quality deblurred results with low computational costs. Both synthetic and real blurred images are tested in the experiments. Encouraging experimental results show that the newly proposed method could effectively restore images blurred by complex motion.