To address the problems of detail loss, color shift and visual quality degradation of images acquired under hazy weather, a fast dehazing algorithm is proposed for estimating atmospheric light veil based on segmental estimation of log-S type function. Firstly, the positive correlation between the atmospheric light veil and the minimum channel of the haze image is obtained by in-depth derivation on the atmospheric scattering model. Then, according to the different haze concentrations in different regions of the haze image, a segmented estimation model is constructed to estimate the atmospheric light veil of the haze image. Finally, the method of local atmospheric light estimation in the middle channel based on median filter optimization is proposed, and the haze-free image is recovered by the atmospheric scattering model. The experimental results show that the new visible edges, average gradient and information entropy of the restored image are increased respectively by 17.4%, 50.5% and 30%, the running time is 17.5% lower than that of the conventional fast dehazing algorithm. The algorithm is able to recover images with complete dehazing, natural colour and significant detail recovery.