A high-order hybrid regularization method for image blind restoration was proposed to restore blurry-noisy images blindly. Because of the sparse edges in a natural image, the Total Variation(TV) regularization restriction was applied to the edge texture component. According to the variation regulation of pixels in homogeneous smooth regions of the natural image, a high-order Tikhonov-like regularization restriction was applied to the smooth regions of the image, and a new model which combines the TV regularization restriction and the high-order Tikhonov-like regularization restriction was proposed. Finally, a multi-variable Split-Bregman (MSB) optimized iterative scheme was proposed to recover the image. A large number of experiments have been performed. The results prove that the proposed method is able to preserve the image edges while avoiding staircase effects and false edges in the smooth regions. The proposed method is compared with several recent image blind restoration methods, and results show that the Increment of Signal-to-noise Ratio(ISNR) has been improved between 0.03 dB and 2.5 dB.