A fast de-blurring variational model for optical remote sensing image is proposed. In the proposed model, the de-blurring and de-nosing parts can be divided into two alternating minimizing processes using surrogated functional decoupling approach. Combined Fourier domain linear de-blurring filtering and subspace projection de-nosing method together, a novel alternating iterative numerical algorithm is proposed. Two classical point spread functions such as atmosphere turbulence Gaussian blurring and out-of-focus blurring are designed to demonstrate this algorithm′s performance. Experimental results show that the improved signal to noise ratio in this algorithm is about 2 dB larger than that of the gradient decreasing (GD) algorithm and the iterative convergent rate is improved more than one order of magnitude.