To solve the problem of color separation of printed images, this paper proposes a black generation algorithm that can maximize the gamut of the CMYK output color space. This proposed method considers the printing gamut space as a CMY color cube and divides it into six sub-gamut spaces using the gamut center diagonal. First, the color targets and algorithms are designed to calculate a gamut center diagonal black lookup table and two gamut boundary black lookup tables for each sub-gamut. Then, for an input color, the three corresponding lookup tables are found by determining the sub-gamut space where the input color is located, and the final CMYK amounts are determined by interpolating the corresponding color points on these lookup tables. Finally, the interpolation calculation results are further optimized using the neighborhood-search strategy. The color-difference evaluation experiment shows that the proposed algorithm can achieve a mean color difference of less than 1 CIEDE2000 standard color-difference unit when reproducing the standard test color target. The gamut reproduction evaluation experiment shows that the gamut distribution and gamut size obtained by the proposed algorithm are closer to the source gamut space than the Gray Balance algorithm. The image reproduction test experiment shows that the proposed algorithm can effectively reproduce the dark details of images and meet the image reproduction requirements of the printing industry.