The paper aims to propose a robust watermarking algorithm based on BSVD decomposition and Radon transform to improve the imperceptibility of watermarking algorithm and the ability of anti-rotation attack. First, the watermarking image was transformed by Arnold transform, then the host image was transformed by NSCT, then the low-frequency sub-block was divided into non-overlapping blocks. Finally, each sub-block was decomposed by BSVD, and the appropriate scaling factor was selected to embed the watermarking into the maximum singular value of the singular matrix. When extracting watermarking, Radon transform was used to correct the host image with the watermarking information, and then the watermarking information was extracted. Experiments showed that the proposed algorithm had good imperceptibility; its PSNR values were above 60 dB; it can resist conventional signal attacks; and its NC values were greater than 0.95. The watermarking algorithm has good imperceptibility and robustness, and has strong ability to resist rotation attack.