The paper aims to propose a digital watermarking algorithm based on Tchebichef moments to solve the problems of large complexity and poor robustness of image moment based watermarking algorithms, especially the sensitivity to scaling and rotation attacks of watermarking which exists in digital watermarking algorithms. Firstly, the non-sampling contourlet transform of the host image was performed to obtain the low frequency sub-band with the same size as the host image. The low frequency sub-band was divided into blocks and singular value decomposition (SVD) was applied on the blocks. According to the characteristics of the singular value, the optimal embedding positions were selected. The embedding strength of the watermarking was calculated adaptively according to the characteristics of the left singular value matrix and the right singular value matrix. The watermark encrypted by Logistic chaos was embedded into the selected singular value to calculate Tchebichf moments of watermarked image for rotation and scaling correction. Experiments show that the algorithm had good invisibility and the NC value of the extracted watermarking reached 0.9386. It can effectively resist rotation and scaling attacks. The algorithm has strong robustness for resistance again rotation attacks at any angle and scaling attacks, and can protect digital products.