We propose a novel blind deconvolution method that consisting of firstly estimating the variance of the Gaussian blur, then performing non-blind deconvolution with the estimated PSF. The main contribution of this paper is the first step - to estimate the variance of the Gaussian blur, by minimizing a novel objective functional: an unbiased estimate of a blur MSE (SURE). The optimal parameter and blur variance are obtained by minimizing this criterion over linear processings that have the form of simple Wiener filterings. We then perform non-blind deconvolution using our recent high-quality SURE-based deconvolution algorithm. The very competitive results show the highly accurate estimation of the blur variance (compared to the ground-truth value) and the great potential of developing more powerful blind deconvolution algorithms based on the SURE-type principle.