In our previous paper, we have developed a projector-Based color matching system for print industry. In this system, a color of print can be matched to the desired color to minimize the color difference between print and projected images. However, in this color matching, it is necessary to observe and measure the projector image under the dark room. In this paper, we proposed a new color correction method for projector image under dim illumination based on the CIECAM02. As well known, in the dim room, the color gamut of reproduced image becomes narrow compared with the gamut in the darkroom. M. Ashdown et al. proposed a method to compress the color gamut in the CIEL*u*v* color space. However, the chromatic adaptation according to the change of white point of the illumination is not considered in this method. Therefore we introduce CIECAM02 for color matching under the dim viewing condition. Chromatic and achromatic channels in CIECAM02 space are calculated from an input image and the chromatic channels are compressed to match the possible projection range of output under the illumination. The images obtained by conventional and proposed algorithms are evaluated by the psychophysical experiment used memory matching. As a result, it was shown that the proposed method can improve the color appearance under dim illumination.