It is challenging to convert a hazy color image into a gray-scale image because the color contrast field of a hazy image is distorted. In this paper, a novel decolorization algorithm is proposed to transfer a hazy image into a distortionrecovered gray-scale image. To recover the color contrast field, the relationship between the restored color contrast and its distorted input is presented in CIELab color space. Based on this restoration, a nonlinear optimization problem is formulated to construct the resultant gray-scale image. A new differentiable approximation solution is introduced to solve this problem with an extension of the Huber loss function. Experimental results show that the proposed algorithm effectively preserves the global luminance consistency while represents the original color contrast in gray-scales, which is very close to the corresponding ground truth gray-scale one.