In order to improve the visual effect of degraded images in foggy environment, a fast dehazing algorithm for single image is proposed based on the degradation model and the dark channel prior estimate. Using dark channel prior estimates the atmospheric transmittance roughly, then using edge preserving filtering estimates the refinement of transmittance, after that try to estimate the sky region in the original image for compensating of the transmission of the region. Finally, according to the estimated atmospheric light and transmissivity, the fog image can be recovered by the atmospheric degradation model. In order to solve the problem that the color of the image is darker, the adaptive histogram equalization method is used. The experimental results show that compared with the existing algorithms, the proposed algorithm can effectively improve the effect of image fogging and speed up the processing speed.