During the process of deblurring image, the ring artifacts are inevitable, which seriously affects the definition of the deblurred image. If the blurring kernel is inaccurate, the ring artifacts will be more serious. By analyzing the gradient distribution histogram of the images during the deblurring process, we demonstrated the necessity of adding the nature image gradient constraint to the image restoration. A variable substitution scheme was established to simplify the computation. According to the calculated data, the impact of ring artifacts is not serious in the synthetic image or the real motion blur image by this approach. And the image gradient distribution of calculation result was closer to the latent image than the RL. Moreover, we cloud get a good result even if the motion deblurring kernel was inaccurate.