For blind image restoration resulted in the boundary ringing effect of image, and the traditional Richardson-Lucy filter is as the algorithm of blind image restoration in this paper. After analyzing the causes of boundary ringing effect caused by blind image restoration, this paper propose a boundary ringing suppression algorithm which is extending the boundary of image called Gradient Smooth boundary conditions (Gradient Smooth BCs). The algorithm of this paper makes the extended image meet the Discrete Fourier requirements of periodical data, and the extended boundary of image does not have a significant edge, so that effectively suppress the boundary ringing effect. Through the digital simulation realizing experimental verification, and the parameter of boundary peak signal to noise ratio (BPSNR) and mean square error (MSE) which is introduced to evaluate the restored image, the experimental results show that the algorithm of this paper can effectively evaluate the ringing effect in restored image. Keywords: blind image restoration; ringing effect; Gradient Smooth boundary conditions; boundary peak signal to noise ratio(BPSNR) ; mean square error(MSE)