Color correction is important in vision applications. We aim to improve conventional transformation with a linear hypothesis of color correction (i.e., von Kries method) by innovatively using a hue-determined matrix. A new model, named the hue-compensated diagonal model (HCDM), is proposed to benefit correcting colors with chromatic-saturated illuminations. Inspired by the chromatic adaptation occurring in the human visual system (HVS), the HCDM reinforces the illuminant complementary color by weighting the von Kries coefficients. These HCDM weighting terms, being illuminant-hue specific based on the relative absorption model (RAM), consist of the proposed hue-chromatic characteristic function with learning parameters. As a result, the HCDM out-performed both the principle component analysis (PCA) approach and the von Kries method in most synthetic experiments, and achieved better results than the von Kries method in real image experiments. Thus, the proposed HCDM, with global-processing capability and real-image applicability, can be used as an effective model in color reproductions and image applications.