We propose a numerical method to determine a transformation of a color space into a hue linear color space with a maximum degree of perceptual uniformity. In a first step, a transformation of the initial color space into a nearly perceptually uniform space is computed using multigrid optimization. In a second step, a hue correction is applied to the resulting color space while preserving the perceptual uniformity as far as possible. The two-stage transformation can be stored as a single lookup table for convenient usage in gamut mapping applications.We evaluated our approach on the CIELAB color space using the CIEDE2000 color-difference formula as a measure of perceptual uniformity and the Hung and Berns data as a reference of constant perceived hue. Our experiments show a mean disagreement of 5.0% and a STRESS index of 9.43 between CIEDE2000 color differences and Euclidean distances in the resulting hue linear color space. Comparisons with the hue linear IPT color space illustrate the performance of our method.