Abstract: A new method for the acceleration of Richardson-Lucy（R-L）iterative image restoration algorithms is given, which is based on the damped RL algorithm and polynomial extrapolation. By storing the latest several (n) results of damped R-L algorithm, a polynomial function is used to analyze these results, and to approximate the relationship among them. Then, this polynomial function is utilized to predict the later results in the iterative process. This method can simplify calculation and accelerate the image restoration algorithms. The method can offer nearly perfect reconstructed image, and is applicable to other relevant algorithms.