Cover lossless robust watermarking technology is one of the frontier hotspots in the field of information hiding. It can fully restore the original image without external attacks, while when there is an attack, it can extract robust watermarks for secure verification. Most of the countermeasures proposed in the literature are robust to geometric attacks, but most schemes are less imperceptible, mainly due to the fixed location of the embeddings. In this paper, we propose a Zernike moments-based robust and reversible watermarking scheme. It embeds robust watermarks in low-order Zernike moments to keep their rotational invariance, thus it can be used for information authentication and is not easy to detect. Then the reversible watermark is embedded outside the robust watermark region as compensation information to fully restore the original image. The proposed scheme enables the image has the ability to restore the image and secure verification at the same time. Theoretical and simulation results show that it has better bit error rate and imperceptibility.