The purpose of blind image deblurring is to recover a clear image from a blurred image by iterating in the case where the blur kernel is unknown. When the real image has fewer dark pixels, the dark channel a priori algorithm does not produce satisfactory results. It is found that the absolute value of the elements in the secondorder gradient (Hessian matrix) decreases as the image is gradually blurred. Using this feature, a model of dark channel a priori blind image deblurring algorithm based on regularized secondorder gradients is proposed. Firstly, the theoretical proofs related to the algorithm are shown, and the feasibility of the Hessian matrix in preserving edge details and image details is experimentally illustrated. Then, a semiquadratic splitting strategy is used to solve the nonconvex optimization problem, and finally, the fast Fourier transform is used to obtain the final clear image and the blurred kernel. The experimental results show that the algorithm can well preserve the edge details and eliminate ringing artifacts while suppressing noise, and it is more robust and performs well than existing image deblurring methods on both synthetic and natural images. The SSIM values are improved by more than 10% on average in the natural image dataset.