The intention of this paper is to specifically propose a color image watermarking method, instead of intuitively applying the watermarking approaches designed for gray-level images to the tri-channel signals of the color host images. Inheriting the good visual quality of the Fibonacci lattice applied in color quantization, the proposed method deploys the Fibonacci lattice points on the chromatic plane, and the fragile watermark message can be thereby embedded by modulating the indexes of lattice points unobtrusively. With another robust watermark embedded into the luminance component by the QIM approach, the hybrid watermarking system embeds two watermark messages with different purposes concurrently, and can thus be applied to various scenarios. Simulation results have shown that the fragile watermark embedded in the chromatic component does not degrade the function of the robust watermark embedded in the luminance component. Moreover, it performs a good capability of authentication, which is able to locate the slight modifications on the watermarked image.