We proposed the regularized iterative restoration method considering relaxation parameter and regularization paramenter in order to restore the noisy motion-blurred images. We used (i-H) as a regularization operator and these two kinds of constraints were applied while conventional regularization iterative restoration method proposed by Jan Biemond et al used the 2-D Laplacian filter and a predetermined regularization parameter value and relaxation parameter to 1. Through the experimental results, we showed better results compared with those by a conventional method and or regularized iterative restoration method just considering only a regularization parameter. These two kinds of constratints have good effects when applied into the regularized iterative restoration method for noisy motion-blurred images.