Considering the frequent occurrence of hazy weather, single image dehazing has become an important research task. Physical model-based and deep learning-based methods are two competitive methods in single image dehazing, but achieving fidelity and effectively removing haze at the same time in real hazy scenes is still a challenging problem. In this work, we propose a mixed iterative model to restore high-quality clear images by integrating a physical model-based approach and a learning-based approach, which can combine the advantages of the physical model-based method in maintaining natural attributes and the advantages of the learning-based method in completely removing haze. For a hazy image, first, according to the haze density, it is divided into separate regions to calculate the local atmospheric light. Then, we utilize the dark channel prior and DehazeNet to jointly estimate the transmission, which can estimate an accurate recovered image that is more in line with the real scene. Finally, a numerical iterative strategy is employed to further optimize the atmospheric light and transmission. The experiments on both synthetic and natural hazy image datasets indicate that the proposed method can restore natural and clean images and has superior performance than other state-of-the-art algorithms in peak signal-to-noise ratio, structural similarity, information entropy, color natural index, and color histogram. And in the four indicators of the quantitative results of the synthetic hazy test set, we achieve the highest score in three of them and the second highest result in another. In the comparison of the two quantitative indicators of natural hazy images, our average objective results are both the highest.INDEX TERMS Image dehazing, numerical iterative, mixed model, joint transmission.