The image-to-device gamut mapping algorithm which takes into account the actual image gamut is able to avoid compressing the image gamut more than necessary thereby better preserve the color appearance. In this paper, a new approach to visualize the image gamut based on Ball-Pivoting Algorithm (BPA) is proposed. First we convert a RGB image to CIEL*a*b* color space using the well-known analytical transformations, then we quantize the color points of image to a grid using the discrete CIEL*a*b* color space. At last the color data sets of the image gamut surface are reconstructed based on the BPA. We demonstrate that image gamut can be computed efficiently on practical data sets of images and at the same time gives an accurate approximation of the image gamut. It will helpful to understand the color transformation mechanism and will beneficial to developing the image-dependent gamut mapping algorithms.