Aiming at the problems of image hue and brightness distortion in sky regions when dealing with fog images by the classic dark channel theory algorithm, we propose a fog image enhancement algorithm based on the boundary constraint weighted least squares filtering. According to the histogram property of fog image, we reduce the boundary condition and obtain the initial transmittance. The transmission is smoothed by weighted least squares filtering method and tolerance mechanism. The enhanced image is obtained by using the model of dark channel theory. The research results show that the proposed algorithm is better than the existing dark channel algorithm in terms of dehazing effect and image visibility.