The work aims to improve the anti-attack performance of color image digital watermarking, including scaling, rotation, translation, noise and so on. A color image digital watermarking algorithm was proposed based on the coordinate transformation and quaternion Fourier transform (QFT). The quaternion color image representation and its bilateral Fourier transform were introduced and the relationship between Cartesian coordinate and polar logarithmic coordinate was analyzed. The low-frequency part of the real component after QFT was chosen as embedded area. In order to improve the algorithm's ability to resist geometric attacks, the relationship of corresponding points between Cartesian coordinate and logarithmic polar coordinate was given. The watermarking embedding and extracting process was described in details. The experiments were carried out with regard to the attacks, such as noise, filtering, shear and so on. The results showed that the algorithm described could improve the accuracy of extracting information and the ability of watermarking against attacks. The algorithm can guarantee the concealment of the watermarking. At the same time, it can resist attacks to a certain degree. Therefore, it will meet the needs of copyright protection and digital anti-counterfeiting.