In this thesis, we propose a new color quantization method which considers not only the population of colors used in an image, but also the individual importance of colors in the respect of human cognition. The importance of a color used in an image can be approximated through summed value measured from the individual pixel contribution to the image. In this thesis, we quantify the importance of a pixel using the value determined by the smoothness and the intensity. Then, the importance of a color used in an image is defined as a sum of importance of pixels with the same color. Because the population of used colors in an image is a dominant factor which influences the image quality, it is required to avoid conflict between the importance of colors and their population. In fact, since the importance of colors in this thesis is a sum of importance of pixels of a color, it can be implicitly regarded as a measure that reflects the population term. This thesis also presents a method to control the proportion of the importance of pixels to a population term in determing quantized image. Experimental results show that the proposed method can generate better quantization than previous method in the respect of a smoothness.