Abstract: Motion deblurring is one of the recovery problems in image restoration, which remains several challenges in kernel estimation and blind deconvolution. This paper proposes a new optimization method for estimating the blurring kernel by gradient enhancement, which can iteratively solve a uniform deblur model. In this model, the point-spread-function(PSF) can be accurately estimated and refined by gradually enhancing the image gradients. Our approach includes following steps: edge-preserving gradient enhancement, edge selection, kernel estimation and refinement, fast non-blind deconvolution. The edge-preserving gradient enhancement can restore sharp edges while have no effect in flat regions. Combined with the edge selection, it greatly helps to estimate the kernel. To improve its speed performance, the estimation and deconvolution steps are executed in frequency domain. Experimental results demonstrate that our method can efficiently produce an accurate blur kernel and a restored image with fine image details.