The work aims to construct a mathematical model based on regression algorithm to determine the best solid density by combining with the dot gain, thus improving the quality of print, regarding the fact that the density is the best when the relative contrast is the largest. The three-dimensional coordinate graph was obtained based on the solid density, relative contrast and dot gain value measured according to the proofs; and based on the regression algorithm, a mathematical model of the functional relationship between relative contrast K, dot gain and solid density was established. The model was used to find the parameter matching algorithm of dot gain and solid density when the relative contrast was maximal. When the dot gain was within 15%~20% of the national standard, the best solid density could be finally determined based on the minimum variance principle. The parameter matching of solid density and dot gain found based on the regression algorithm conformed to the function y=ax+b when the relative contrast was maximal, and the best solid densities of C, M, Y, and BK inks were respectively 1.551, 1.612, 0.975 and 1.828. The method to determine the best solid density based on the regression algorithm can ensure good relative contrast and appropriate dot gain, and improve the clarity and vividness of the prints. It is of certain guiding significance for the printing quality control.