The work aims to arrange the image pixels based on hue angle clustering method, so as to quickly and accurately extracting image color gamut boundary. In the spherical coordinates of device independent color space, pixels in the image were arranged in the descending order according to color attribute values, then, gamut boundary points were extracted from the image according to boundary point features. Based on the image pixels arranged above, the “image-to-device” gamut mapping was calculated. With respect to the image selected by the experiment, the proposed plan could extract the image boundary points accurately, with an average calculating time of only 2.6 s. The image boundary points were calculated in the local maximum gamut boundary description method (SMGBD) recommended by CIE, with the average error more than 3ΔEab* and the average calculating time greater than 1 min. The gamut mapping of the minimum color difference method based on the image pixels arranged by hue angle clustering greatly improved the calculation speed. The method extracting image color gamut boundary points based on hue angle clustering can quickly extract the image boundary points with zero error. Based on that, the gamut mapping was calculated. Such calculation removes the redundant computation and improves the calculation speed, which has great significance for developing the image-to-device gamut mapping.