The work aims to design a robust image watermarking algorithm based on directional pyramid decomposition and stable geometric distortion correction, in order to improve the watermarking algorithm's ability of resisting geometric attacks and give consideration to both higher robustness and insensitivity. Firstly, the directional pyramid was introduced to decompose the carrier image for outputting the corresponding low pass and high pass subbands. Subsequently, the low pass subbands were divided into a series of non-overlapping blocks. According to the brightness, texture and edge mask of the carrier, the embedding strength of the watermark was calculated to balance the imperceptibility and robustness of the watermark image to the maximum extent. Then, the watermark embedding method was designed to embed the watermark encrypted by Arnold map into the non-overlapping subblocks, and the watermark image was obtained by modifying the decomposition coefficient of directional pyramid in the carrier. The training samples were established by applying different attack types to watermark image. The directional pyramid was then used to decompose the training samples for calculating the Gauss Hermite moment energy of the high pass subbands, which was regarded as the feature vector. Then, the feature vector was used to train the fuzzy support vector machine for predicting the geometric distortion parameters and accurately correcting the attacked watermark image. Finally, the watermark detection mechanism was designed to restore the watermark from the watermark image. The experimental data showed that, compared with the current image watermarking scheme, the proposed algorithm had a higher anti-geometric transformation ability, as well as better imperceptibility and robustness with the least distortion degree of extracted watermark, with the corresponding peak signal to noise ratio (PSNR) maintained above 40 dB. The proposed watermarking algorithm has higher robustness and visual insensitivity, which has certain reference value in copyright protection, information security and other fields.