Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary A = B = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc.