This paper presents a robust color image watermarking algorithm based on fuzzy least squares support vector machine (FLS-SVM) and Bessel K form (BKF) distribution, which is a recently developed geometric correction algorithm. We firstly compute the quaternion discrete Fourier transform (QDFT) of the maximum central region of the original color image. Then the watermark is embedded into the magnitudes of low-frequency information of QDFT. In watermark decoding process, the synchronous correction based on FLS-SVM model is used. When training the FLS-SVM model, we firstly perform the quaternion wavelet transform (QWT) of the grayscale images that correspond to the color training images, and then use BKF distribution to fit the empirical histogram of coefficients of the QWT, and finally use the shape parameters and scale parameters of BKF distribution to construct image feature vector. Experimental results show that the proposed algorithm is not only invisible, but also has outstanding robustness against common image processing attacks and geometric attacks.