In the field of image defogging, it is difficult for most defogging models to maintain a balance between accuracy and efficiency. Specifically, high-precision models are often accompanied by complex network structures, and simple network structures often lead to low-quality results. To address the problem, we propose a multi-branch defogging network based on fog concentration classification and dark and bright channel priors. The model uses the defogging networks with different complexity to handle the images with different fog concentrations, which significantly raises the computational efficiency under ensuring the defogging precision. The model is composed of a lightweight foggy image classifier and a multi-branch defogging network. The classifier divides the foggy images into light, medium and dense foggy images and outputs the fog concentration labels. The multi-branch network contains three branches with the same structure but different widths that process three types of fog images separately. We propose a new fog concentration classification method and a new fog concentration classification loss function. The function combines the dark channel characteristics and defogging difficulty of the foggy image with the defogging precision and computational efficiency of the model, so as to obtain a reasonable fog concentration classification, and consequently achieve a good balance of defogging quality and computing power requirements. We propose a new dark channel prior loss function and a new bright channel prior loss function to constrain the multi-branch defogging network, which effectively enhance the defogging precision. Extensive experiments show that the model is beneficial to get better defogging effect with lower network parameters and complexity.