For exact color reproduction between printing matter and projected image, it is necessary to match the color on absolute XYZ color space. However, the color value of each pixel is affected by stray light from the surrounding pixels which is due to the multi-reflection of optical lens in projector. In this paper, we analyzed the influence of each color value between printing matter and projected image, and modeled the relationship. This model became possible to estimate the color change of projected image. Using this estimation, the color of image is corrected to match the printing matter. We demonstrate the proposed method for the print of Macbeth color checker and shows that the model is effective for color matching of projected images.