This paper studies the color to grayscale image conversion algorithms based on global mapping using linear combination of RGB color components. According to the statistical information of the color pixels in the different color components, the combination weights of different components are automatically generated to mapping color to grayscale. In combination with the subjective and objective image quality standards, we present an adaptive global mapping algorithm. Experimental results show that the new algorithm can perform as good as traditional color to grayscale algorithm on the majority of test images, but can outperform the traditional algorithm in case of dominant colors appears in the original image, and significantly improve the visual effect of the gray-scale image.