Bamboo slips image watermarking is a key technology for copyright protection, tampering detection and integrity protection of image data. However, most of the image watermarking keys currently lack the supervision of authoritative institutions, which fails to achieve a good balance between perceived transparency and security. This paper takes the digital images of bamboo slips provided by Gansu Bamboo Slips Museum as the research object, and proposes a reversible hiding watermarking algorithm based on the mean value theorem of divided difference. The watermark key is generated by the combination of the authority department and the department of bamboo slips. In view of the uneven distribution of texture and color of bamboo slips after excavation, different watermark key information after splitting is embedded into the RGB three-channel of bamboo Slips image based on the mean value theorem of divided difference. When the least significant bit (LSB) is replaced, the security and perception transparency of the watermark key information are further improved by using Logistic mapping. The experimental results show that the watermark embedded by the proposed algorithm has good invisibility, and the algorithm has high positioning accuracy for tampered positions of the attacked image.