Data hiding techniques have been widely used to preserve privacy information in the current age media rich systems. Histogram-shifting (HS) is an efficient reversible data hiding (RDH) technique by modifying cover image's pixel-intensity-histogram (PIH) of a certain dimension. By HS, it is more desirable to take high-dimensional PIH to design RDH since image redundancy can be better exploited in this case. Referred to the recently proposed general framework of HS-based RDH, a new RDH scheme based on three-dimensional PIH modification is proposed in this paper. The cover image is first divided into non-overlapping pixel triples to generate a three-dimensional PIH, and then each triple is utilized for data embedding based on an advisable triple classification. In addition, in the histogram generation stage, a pixel selection technique is adopted such that only smooth triples are collected to generate the three-dimensional PIH to further improve the embedding performance. The superiority of our scheme over some state-of-the-art works is experimentally verified.