To solve the data security problem of satellite images, a robust watermarking scheme combining invariant feature points with SVD is proposed. Firstly, SURF feature points are detected in the carrier image, and the feature regions for embedding watermark bits are selected by combining robustness and variance. Then, the preferred regions are normalized and blocked, and each subblock is performed by two-level contourlet transform (CT), and the low-frequency coefficients matrix is selected for SVD transform. Finally, the scrambled quick response (QR) code binary watermark is embedded in a weighted manner. Watermark detection is the inverse process of watermark embedding, which can be completed using a secret key. Experimental results show that the proposed scheme has good robustness against conventional attacks such as noise, filtering, JPEG compression, and geometric attacks such as rotation, scaling, translation, and shearing. It can provide effective protection for the data security of satellite images.