Preserving hue is an important issue for color image processing. In order to preserve hue, color image processing is often carried out in HSI or HSV color space which is translated from RGB color space. Transforming from RGB color space to another and processing in these spaces usually generate gamut problem. We propose image enhancement algorithms which conserve hue and preserve the range (gamut) of the R, G, B channels. First we show an intensity processing method while preserving hue and saturation. In this method, arbitrary gray-scale transform functions can be applied in the intensity component. Next, a hue and intensity preserving saturation mapping method is proposed. Arbitrary gray-scale methods can be also applied in the saturation mapping. Finally, we combine two methods and realize the hue-preserving color image processing with a high arbitrariness without gamut problem. Numerical results confirm our theoretical results and show that our processing scheme performs much better than the conventional hue-preserving methods.