In this paper, a local-moment-driven robust reversible data hiding (LM-RRDH) scheme is proposed, which can provide security to hidden messages against unintentional modifications. The proposed LM-RRDH decomposes an image into LSB and MSB planes and then embeds the secret information into the MSB image so that intrusion by unintentional modifications can be avoided. In addition, the proposed scheme utilizes the prevalent correlation among the pixels on the MSB plane for optimal embedding. In the proposed scheme, a cover image is partitioned into sub-blocks at first, and pixel groups in the sub-block are formed according to local moment and moment-of-moment so that similar-intensity pixels can be grouped into the same group. Next, the secret data is embedded into the pixels of each group by selecting a pairwise embedding strategy adaptively which is based on the number of pixels in each group. As a result, the proposed LM-RRDH can limit the distortion while providing a decent embedding capacity. Further, a protection against non-malicious attacks such as Joint Photographic Experts Group (JPEG) compression is also provided. The experimental results show that the proposed scheme provides a superior quality to the previous works while providing a comparable embedding capacity.