Aiming at these problems of unclear targets， unobvious details， and lower resolution of images captured by imaging equipment under foggy conditions， an image dehazing algorithm based on atmospheric veil constraints and piecewise adjustment was proposed. Firstly， basic unequal relation of the atmospheric veil was mapped to plane model of square and its inscribed circle to obtain the constrained initial atmospheric veil. Then saturation approximation was used to get a rough atmospheric veil to blur the edge information. Meanwhile， gradient constraint was also introduced to detect the edge cost， which was utilized to correct initial atmospheric veil. In order to improve the distortion of images with close region and the incomplete defogging of images with distant region， an adaptive piecewise adjustment function was proposed to optimize the atmospheric veil. Finally， a clear image was obtained by the restoration module. Experimental results show that the proposed algorithm can be applied to all kinds of images， and has better defogging effect compared to some classic algorithms。It not only maintains the original images'characteristics， but also obtains the restored image with bright， clear and natural colors， and has advantages in various indicators.